Sample records for sparse signal reconstruction
l1- and l2-Norm Joint Regularization Based Sparse Signal Reconstruction Scheme
Chanzi Liu
Full Text Available Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations. This is also the application condition of compressive sensing (CS which can find the sparse solution from the measurements far less than the original signal. In this paper, we propose l1- and l2-norm joint regularization based reconstruction framework to approach the original l0-norm based sparseness-inducing constrained sparse signal reconstruction problem. Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem with l0-norm regularization item. Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error than l1-norm relaxation approaches can be realized by using the proposed scheme in most cases. Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach.
Performance bounds for sparse signal reconstruction with multiple side information [arXiv
Luong, Huynh Van; Seiler, Jurgen; Kaup, Andre
In the context of compressive sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information (SI). To address this problem, we propose a reconstruction algorithm with multiple SI (RAMSI) that solves...
Structure-based bayesian sparse reconstruction
Quadeer, Ahmed Abdul; Al-Naffouri, Tareq Y.
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical
Quadeer, Ahmed Abdul
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is very low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at high sparsity. © 1991-2012 IEEE.
Demonstration of Sparse Signal Reconstruction for Radar Imaging of Ice Sheets
Heister, Anton; Scheiber, Rolf
Conventional processing of ice-sounder data produces 2-D images of the ice sheet and bed, where the two dimensions are along-track and depth, while the across-track direction is fixed to nadir. The 2-D images contain information about the topography and radar reflectivity of the ice sheet's surface, bed, and internal layers in the along-track direction. Having multiple antenna phase centers in the across-track direction enables the production of 3-D images of the ice sheet and bed. Compared to conventional 2-D images, these contain additional information about the surface and bed topography, and orientation of the internal layers over a swath in the across-track direction. We apply a 3-D SAR tomographic ice-sounding method based on sparse signal reconstruction [1] to the data collected by Center for Remote Sensing of Ice Sheets (CReSIS) in 2008 in Greenland [2] using their multichannel coherent radar depth sounder (MCoRDS). The MCoRDS data have 16 effective phase centers which allows us to better understand the performance of the method. Lastly we offer sparsity improvement by including wavelet dictionaries into the reconstruction.The results show improved scene feature resolvability in across-track direction compared to MVDR beamformer. References: [1] A. Heister, R. Scheiber, "First Analysis of Sparse Signal Reconstruction for Radar Imaging of Ice Sheets". In: Proceedings of EUSAR, pp. 788-791, June 2016. [2] X. Wu, K. C. Jezek, E. Rodriguez, S. Gogineni, F. Rodriguez-Morales, and A. Freeman, "Ice sheet bed mapping with airborne SAR tomography". IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 10 Part 1, pp. 3791-3802, 2011.
Multichannel Signals Reconstruction Based on Tunable Q-Factor Wavelet Transform-Morphological Component Analysis and Sparse Bayesian Iteration for Rotating Machines
Qing Li
Full Text Available High-speed remote transmission and large-capacity data storage are difficult issues in signals acquisition of rotating machines condition monitoring. To address these concerns, a novel multichannel signals reconstruction approach based on tunable Q-factor wavelet transform-morphological component analysis (TQWT-MCA and sparse Bayesian iteration algorithm combined with step-impulse dictionary is proposed under the frame of compressed sensing (CS. To begin with, to prevent the periodical impulses loss and effectively separate periodical impulses from the external noise and additive interference components, the TQWT-MCA method is introduced to divide the raw vibration signal into low-resonance component (LRC, i.e., periodical impulses and high-resonance component (HRC, thus, the periodical impulses are preserved effectively. Then, according to the amplitude range of generated LRC, the step-impulse dictionary atom is designed to match the physical structure of periodical impulses. Furthermore, the periodical impulses and HRC are reconstructed by the sparse Bayesian iteration combined with step-impulse dictionary, respectively, finally, the final reconstructed raw signals are obtained by adding the LRC and HRC, meanwhile, the fidelity of the final reconstructed signals is tested by the envelop spectrum and error analysis, respectively. In this work, the proposed algorithm is applied to simulated signal and engineering multichannel signals of a gearbox with multiple faults. Experimental results demonstrate that the proposed approach significantly improves the reconstructive accuracy compared with the state-of-the-art methods such as non-convex Lq (q = 0.5 regularization, spatiotemporal sparse Bayesian learning (SSBL and L1-norm, etc. Additionally, the processing time, i.e., speed of storage and transmission has increased dramatically, more importantly, the fault characteristics of the gearbox with multiple faults are detected and saved, i.e., the
Sparse Image Reconstruction in Computed Tomography
Jørgensen, Jakob Sauer
In recent years, increased focus on the potentially harmful effects of x-ray computed tomography (CT) scans, such as radiation-induced cancer, has motivated research on new low-dose imaging techniques. Sparse image reconstruction methods, as studied for instance in the field of compressed sensing...... applications. This thesis takes a systematic approach toward establishing quantitative understanding of conditions for sparse reconstruction to work well in CT. A general framework for analyzing sparse reconstruction methods in CT is introduced and two sets of computational tools are proposed: 1...... contributions to a general set of computational characterization tools. Thus, the thesis contributions help advance sparse reconstruction methods toward routine use in...
The application of sparse linear prediction dictionary to compressive sensing in speech signals
YOU Hanxu
Full Text Available Appling compressive sensing (CS,which theoretically guarantees that signal sampling and signal compression can be achieved simultaneously,into audio and speech signal processing is one of the most popular research topics in recent years.In this paper,K-SVD algorithm was employed to learn a sparse linear prediction dictionary regarding as the sparse basis of underlying speech signals.Compressed signals was obtained by applying random Gaussian matrix to sample original speech frames.Orthogonal matching pursuit (OMP and compressive sampling matching pursuit (CoSaMP were adopted to recovery original signals from compressed one.Numbers of experiments were carried out to investigate the impact of speech frames length,compression ratios,sparse basis and reconstruction algorithms on CS performance.Results show that sparse linear prediction dictionary can advance the performance of speech signals reconstruction compared with discrete cosine transform (DCT matrix.
High-SNR spectrum measurement based on Hadamard encoding and sparse reconstruction
Wang, Zhaoxin; Yue, Jiang; Han, Jing; Li, Long; Jin, Yong; Gao, Yuan; Li, Baoming
The denoising capabilities of the H-matrix and cyclic S-matrix based on the sparse reconstruction, employed in the Pixel of Focal Plane Coded Visible Spectrometer for spectrum measurement are investigated, where the spectrum is sparse in a known basis. In the measurement process, the digital micromirror device plays an important role, which implements the Hadamard coding. In contrast with Hadamard transform spectrometry, based on the shift invariability, this spectrometer may have the advantage of a high efficiency. Simulations and experiments show that the nonlinear solution with a sparse reconstruction has a better signal-to-noise ratio than the linear solution and the H-matrix outperforms the cyclic S-matrix whether the reconstruction method is nonlinear or linear.
Efficient Sparse Signal Transmission over a Lossy Link Using Compressive Sensing
Liantao Wu
Full Text Available Reliable data transmission over lossy communication link is expensive due to overheads for error protection. For signals that have inherent sparse structures, compressive sensing (CS is applied to facilitate efficient sparse signal transmissions over lossy communication links without data compression or error protection. The natural packet loss in the lossy link is modeled as a random sampling process of the transmitted data, and the original signal will be reconstructed from the lossy transmission results using the CS-based reconstruction method at the receiving end. The impacts of packet lengths on transmission efficiency under different channel conditions have been discussed, and interleaving is incorporated to mitigate the impact of burst data loss. Extensive simulations and experiments have been conducted and compared to the traditional automatic repeat request (ARQ interpolation technique, and very favorable results have been observed in terms of both accuracy of the reconstructed signals and the transmission energy consumption. Furthermore, the packet length effect provides useful insights for using compressed sensing for efficient sparse signal transmission via lossy links.
Homotopic non-local regularized reconstruction from sparse positron emission tomography measurements
Wong, Alexander; Liu, Chenyi; Wang, Xiao Yu; Fieguth, Paul; Bie, Hongxia
Positron emission tomography scanners collect measurements of a patient's in vivo radiotracer distribution. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule, and the tomograms must be reconstructed from projections. The reconstruction of tomograms from the acquired PET data is an inverse problem that requires regularization. The use of tightly packed discrete detector rings, although improves signal-to-noise ratio, are often associated with high costs of positron emission tomography systems. Thus a sparse reconstruction, which would be capable of overcoming the noise effect while allowing for a reduced number of detectors, would have a great deal to offer. In this study, we introduce and investigate the potential of a homotopic non-local regularization reconstruction framework for effectively reconstructing positron emission tomograms from such sparse measurements. Results obtained using the proposed approach are compared with traditional filtered back-projection as well as expectation maximization reconstruction with total variation regularization. A new reconstruction method was developed for the purpose of improving the quality of positron emission tomography reconstruction from sparse measurements. We illustrate that promising reconstruction performance can be achieved for the proposed approach even at low sampling fractions, which allows for the use of significantly fewer detectors and have the potential to reduce scanner costs
Designing sparse sensing matrix for compressive sensing to reconstruct high resolution medical images
Vibha Tiwari
Full Text Available Compressive sensing theory enables faithful reconstruction of signals, sparse in domain $ \\Psi $, at sampling rate lesser than Nyquist criterion, while using sampling or sensing matrix $ \\Phi $ which satisfies restricted isometric property. The role played by sensing matrix $ \\Phi $ and sparsity matrix $ \\Psi $ is vital in faithful reconstruction. If the sensing matrix is dense then it takes large storage space and leads to high computational cost. In this paper, effort is made to design sparse sensing matrix with least incurred computational cost while maintaining quality of reconstructed image. The design approach followed is based on sparse block circulant matrix (SBCM with few modifications. The other used sparse sensing matrix consists of 15 ones in each column. The medical images used are acquired from US, MRI and CT modalities. The image quality measurement parameters are used to compare the performance of reconstructed medical images using various sensing matrices. It is observed that, since Gram matrix of dictionary matrix ($ \\Phi \\Psi \\mathrm{} $ is closed to identity matrix in case of proposed modified SBCM, therefore, it helps to reconstruct the medical images of very good quality.
Bound on the estimation grid size for sparse reconstruction in direction of arrival estimation
Coutiño Minguez, M.A.; Pribic, R; Leus, G.J.T.
A bound for sparse reconstruction involving both the signal-to-noise ratio (SNR) and the estimation grid size is presented. The bound is illustrated for the case of a uniform linear array (ULA). By reducing the number of possible sparse vectors present in the feasible set of a constrained â""1-norm
Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise
Orović, Irena; Stanković, Srdjan; Amin, Moeness
A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases of monocomponent and multicomponent signals.
Atmospheric inverse modeling via sparse reconstruction
Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten
Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.
Signal Sampling for Efficient Sparse Representation of Resting State FMRI Data
Ge, Bao; Makkie, Milad; Wang, Jin; Zhao, Shijie; Jiang, Xi; Li, Xiang; Lv, Jinglei; Zhang, Shu; Zhang, Wei; Han, Junwei; Guo, Lei; Liu, Tianming
As the size of brain imaging data such as fMRI grows explosively, it provides us with unprecedented and abundant information about the brain. How to reduce the size of fMRI data but not lose much information becomes a more and more pressing issue. Recent literature studies tried to deal with it by dictionary learning and sparse representation methods, however, their computation complexities are still high, which hampers the wider application of sparse representation method to large scale fMRI datasets. To effectively address this problem, this work proposes to represent resting state fMRI (rs-fMRI) signals of a whole brain via a statistical sampling based sparse representation. First we sampled the whole brain's signals via different sampling methods, then the sampled signals were aggregate into an input data matrix to learn a dictionary, finally this dictionary was used to sparsely represent the whole brain's signals and identify the resting state networks. Comparative experiments demonstrate that the proposed signal sampling framework can speed-up by ten times in reconstructing concurrent brain networks without losing much information. The experiments on the 1000 Functional Connectomes Project further demonstrate its effectiveness and superiority. PMID:26646924
Sparse Reconstruction of Regional Gravity Signal Based on Stabilized Orthogonal Matching Pursuit (SOMP)
Saadat, S. A.; Safari, A.; Needell, D.
The main role of gravity field recovery is the study of dynamic processes in the interior of the Earth especially in exploration geophysics. In this paper, the Stabilized Orthogonal Matching Pursuit (SOMP) algorithm is introduced for sparse reconstruction of regional gravity signals of the Earth. In practical applications, ill-posed problems may be encountered regarding unknown parameters that are sensitive to the data perturbations. Therefore, an appropriate regularization method needs to be applied to find a stabilized solution. The SOMP algorithm aims to regularize the norm of the solution vector, while also minimizing the norm of the corresponding residual vector. In this procedure, a convergence point of the algorithm that specifies optimal sparsity-level of the problem is determined. The results show that the SOMP algorithm finds the stabilized solution for the ill-posed problem at the optimal sparsity-level, improving upon existing sparsity based approaches.
Joint-2D-SL0 Algorithm for Joint Sparse Matrix Reconstruction
Dong Zhang
Full Text Available Sparse matrix reconstruction has a wide application such as DOA estimation and STAP. However, its performance is usually restricted by the grid mismatch problem. In this paper, we revise the sparse matrix reconstruction model and propose the joint sparse matrix reconstruction model based on one-order Taylor expansion. And it can overcome the grid mismatch problem. Then, we put forward the Joint-2D-SL0 algorithm which can solve the joint sparse matrix reconstruction problem efficiently. Compared with the Kronecker compressive sensing method, our proposed method has a higher computational efficiency and acceptable reconstruction accuracy. Finally, simulation results validate the superiority of the proposed method.
Sparse BLIP: BLind Iterative Parallel imaging reconstruction using compressed sensing.
She, Huajun; Chen, Rong-Rong; Liang, Dong; DiBella, Edward V R; Ying, Leslie
To develop a sensitivity-based parallel imaging reconstruction method to reconstruct iteratively both the coil sensitivities and MR image simultaneously based on their prior information. Parallel magnetic resonance imaging reconstruction problem can be formulated as a multichannel sampling problem where solutions are sought analytically. However, the channel functions given by the coil sensitivities in parallel imaging are not known exactly and the estimation error usually leads to artifacts. In this study, we propose a new reconstruction algorithm, termed Sparse BLind Iterative Parallel, for blind iterative parallel imaging reconstruction using compressed sensing. The proposed algorithm reconstructs both the sensitivity functions and the image simultaneously from undersampled data. It enforces the sparseness constraint in the image as done in compressed sensing, but is different from compressed sensing in that the sensing matrix is unknown and additional constraint is enforced on the sensitivities as well. Both phantom and in vivo imaging experiments were carried out with retrospective undersampling to evaluate the performance of the proposed method. Experiments show improvement in Sparse BLind Iterative Parallel reconstruction when compared with Sparse SENSE, JSENSE, IRGN-TV, and L1-SPIRiT reconstructions with the same number of measurements. The proposed Sparse BLind Iterative Parallel algorithm reduces the reconstruction errors when compared to the state-of-the-art parallel imaging methods. Copyright © 2013 Wiley Periodicals, Inc.
Split-Bregman-based sparse-view CT reconstruction
Vandeghinste, Bert; Vandenberghe, Stefaan [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Goossens, Bart; Pizurica, Aleksandra; Philips, Wilfried [Ghent Univ. (Belgium). Image Processing and Interpretation Research Group (IPI); Beenhouwer, Jan de [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Antwerp Univ., Wilrijk (Belgium). The Vision Lab; Staelens, Steven [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Antwerp Univ., Edegem (Belgium). Molecular Imaging Centre Antwerp
Total variation minimization has been extensively researched for image denoising and sparse view reconstruction. These methods show superior denoising performance for simple images with little texture, but result in texture information loss when applied to more complex images. It could thus be beneficial to use other regularizers within medical imaging. We propose a general regularization method, based on a split-Bregman approach. We show results for this framework combined with a total variation denoising operator, in comparison to ASD-POCS. We show that sparse-view reconstruction and noise regularization is possible. This general method will allow us to investigate other regularizers in the context of regularized CT reconstruction, and decrease the acquisition times in {mu}CT. (orig.)
Task-based data-acquisition optimization for sparse image reconstruction systems
Chen, Yujia; Lou, Yang; Kupinski, Matthew A.; Anastasio, Mark A.
Conventional wisdom dictates that imaging hardware should be optimized by use of an ideal observer (IO) that exploits full statistical knowledge of the class of objects to be imaged, without consideration of the reconstruction method to be employed. However, accurate and tractable models of the complete object statistics are often difficult to determine in practice. Moreover, in imaging systems that employ compressive sensing concepts, imaging hardware and (sparse) image reconstruction are innately coupled technologies. We have previously proposed a sparsity-driven ideal observer (SDIO) that can be employed to optimize hardware by use of a stochastic object model that describes object sparsity. The SDIO and sparse reconstruction method can therefore be "matched" in the sense that they both utilize the same statistical information regarding the class of objects to be imaged. To efficiently compute SDIO performance, the posterior distribution is estimated by use of computational tools developed recently for variational Bayesian inference. Subsequently, the SDIO test statistic can be computed semi-analytically. The advantages of employing the SDIO instead of a Hotelling observer are systematically demonstrated in case studies in which magnetic resonance imaging (MRI) data acquisition schemes are optimized for signal detection tasks.
Machinery vibration signal denoising based on learned dictionary and sparse representation
Guo, Liang; Gao, Hongli; Li, Jun; Huang, Haifeng; Zhang, Xiaochen
Mechanical vibration signal denoising has been an import problem for machine damage assessment and health monitoring. Wavelet transfer and sparse reconstruction are the powerful and practical methods. However, those methods are based on the fixed basis functions or atoms. In this paper, a novel method is presented. The atoms used to represent signals are learned from the raw signal. And in order to satisfy the requirements of real-time signal processing, an online dictionary learning algorithm is adopted. Orthogonal matching pursuit is applied to extract the most pursuit column in the dictionary. At last, denoised signal is calculated with the sparse vector and learned dictionary. A simulation signal and real bearing fault signal are utilized to evaluate the improved performance of the proposed method through the comparison with kinds of denoising algorithms. Then Its computing efficiency is demonstrated by an illustrative runtime example. The results show that the proposed method outperforms current algorithms with efficiency calculation. (paper)
Sparse reconstruction using distribution agnostic bayesian matching pursuit
Masood, Mudassir
A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.
Point-source reconstruction with a sparse light-sensor array for optical TPC readout
Rutter, G; Richards, M; Bennieston, A J; Ramachers, Y A
A reconstruction technique for sparse array optical signal readout is introduced and applied to the generic challenge of large-area readout of a large number of point light sources. This challenge finds a prominent example in future, large volume neutrino detector studies based on liquid argon. It is concluded that the sparse array option may be ruled out for reasons of required number of channels when compared to a benchmark derived from charge readout on wire-planes. Smaller-scale detectors, however, could benefit from this technology.
Masood, Mudassir; Al-Naffouri, Tareq Y.
A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics
A modified sparse reconstruction method for three-dimensional synthetic aperture radar image
Zhang, Ziqiang; Ji, Kefeng; Song, Haibo; Zou, Huanxin
There is an increasing interest in three-dimensional Synthetic Aperture Radar (3-D SAR) imaging from observed sparse scattering data. However, the existing 3-D sparse imaging method requires large computing times and storage capacity. In this paper, we propose a modified method for the sparse 3-D SAR imaging. The method processes the collection of noisy SAR measurements, usually collected over nonlinear flight paths, and outputs 3-D SAR imagery. Firstly, the 3-D sparse reconstruction problem is transformed into a series of 2-D slices reconstruction problem by range compression. Then the slices are reconstructed by the modified SL0 (smoothed l0 norm) reconstruction algorithm. The improved algorithm uses hyperbolic tangent function instead of the Gaussian function to approximate the l0 norm and uses the Newton direction instead of the steepest descent direction, which can speed up the convergence rate of the SL0 algorithm. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm. It is shown that our method, compared with existing 3-D sparse imaging method, performs better in reconstruction quality and the reconstruction time.
A Novel Design of Sparse Prototype Filter for Nearly Perfect Reconstruction Cosine-Modulated Filter Banks
Wei Xu
Full Text Available Cosine-modulated filter banks play a major role in digital signal processing. Sparse FIR filter banks have lower implementation complexity than full filter banks, while keeping a good performance level. This paper presents a fast design paradigm for sparse nearly perfect-reconstruction (NPR cosine-modulated filter banks. First, an approximation function is introduced to reduce the non-convex quadratically constrained optimization problem to a linearly constrained optimization problem. Then, the desired sparse linear phase FIR prototype filter is derived through the orthogonal matching pursuit (OMP performed under the weighted l 2 norm. The simulation results demonstrate that the proposed scheme is an effective paradigm to design sparse NPR cosine-modulated filter banks.
Sparse dictionary for synthetic transmit aperture medical ultrasound imaging.
Wang, Ping; Jiang, Jin-Yang; Li, Na; Luo, Han-Wu; Li, Fang; Cui, Shi-Gang
It is possible to recover a signal below the Nyquist sampling limit using a compressive sensing technique in ultrasound imaging. However, the reconstruction enabled by common sparse transform approaches does not achieve satisfactory results. Considering the ultrasound echo signal's features of attenuation, repetition, and superposition, a sparse dictionary with the emission pulse signal is proposed. Sparse coefficients in the proposed dictionary have high sparsity. Images reconstructed with this dictionary were compared with those obtained with the three other common transforms, namely, discrete Fourier transform, discrete cosine transform, and discrete wavelet transform. The performance of the proposed dictionary was analyzed via a simulation and experimental data. The mean absolute error (MAE) was used to quantify the quality of the reconstructions. Experimental results indicate that the MAE associated with the proposed dictionary was always the smallest, the reconstruction time required was the shortest, and the lateral resolution and contrast of the reconstructed images were also the closest to the original images. The proposed sparse dictionary performed better than the other three sparse transforms. With the same sampling rate, the proposed dictionary achieved excellent reconstruction quality.
Wavefront reconstruction in digital off-axis holography via sparse coding of amplitude and absolute phase.
Katkovnik, V; Shevkunov, I A; Petrov, N V; Egiazarian, K
This work presents the new method for wavefront reconstruction from a digital hologram recorded in off-axis configuration. The main feature of the proposed algorithm is a good ability for noise filtration due to the original formulation of the problem taking into account the presence of noise in the recorded intensity distribution and the sparse phase and amplitude reconstruction approach with the data-adaptive block-matching 3D technique. Basically, the sparsity assumes that low dimensional models can be used for phase and amplitude approximations. This low dimensionality enables strong suppression of noisy components and accurate revealing of the main features of the signals of interest. The principal point is that dictionaries of these sparse models are not known in advance and reconstructed from given noisy observations in a multiobjective optimization procedure. We show experimental results demonstrating the effectiveness of our approach.
Hierarchical Bayesian sparse image reconstruction with application to MRFM.
Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves
This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.
Real-time SPARSE-SENSE cardiac cine MR imaging: optimization of image reconstruction and sequence validation.
Goebel, Juliane; Nensa, Felix; Bomas, Bettina; Schemuth, Haemi P; Maderwald, Stefan; Gratz, Marcel; Quick, Harald H; Schlosser, Thomas; Nassenstein, Kai
Improved real-time cardiac magnetic resonance (CMR) sequences have currently been introduced, but so far only limited practical experience exists. This study aimed at image reconstruction optimization and clinical validation of a new highly accelerated real-time cine SPARSE-SENSE sequence. Left ventricular (LV) short-axis stacks of a real-time free-breathing SPARSE-SENSE sequence with high spatiotemporal resolution and of a standard segmented cine SSFP sequence were acquired at 1.5 T in 11 volunteers and 15 patients. To determine the optimal iterations, all volunteers' SPARSE-SENSE images were reconstructed using 10-200 iterations, and contrast ratios, image entropies, and reconstruction times were assessed. Subsequently, the patients' SPARSE-SENSE images were reconstructed with the clinically optimal iterations. LV volumetric values were evaluated and compared between both sequences. Sufficient image quality and acceptable reconstruction times were achieved when using 80 iterations. Bland-Altman plots and Passing-Bablok regression showed good agreement for all volumetric parameters. 80 iterations are recommended for iterative SPARSE-SENSE image reconstruction in clinical routine. Real-time cine SPARSE-SENSE yielded comparable volumetric results as the current standard SSFP sequence. Due to its intrinsic low image acquisition times, real-time cine SPARSE-SENSE imaging with iterative image reconstruction seems to be an attractive alternative for LV function analysis. • A highly accelerated real-time CMR sequence using SPARSE-SENSE was evaluated. • SPARSE-SENSE allows free breathing in real-time cardiac cine imaging. • For clinically optimal SPARSE-SENSE image reconstruction, 80 iterations are recommended. • Real-time SPARSE-SENSE imaging yielded comparable volumetric results as the reference SSFP sequence. • The fast SPARSE-SENSE sequence is an attractive alternative to standard SSFP sequences.
A fast sparse reconstruction algorithm for electrical tomography
Zhao, Jia; Xu, Yanbin; Tan, Chao; Dong, Feng
Electrical tomography (ET) has been widely investigated due to its advantages of being non-radiative, low-cost and high-speed. However, the image reconstruction of ET is a nonlinear and ill-posed inverse problem and the imaging results are easily affected by measurement noise. A sparse reconstruction algorithm based on L 1 regularization is robust to noise and consequently provides a high quality of reconstructed images. In this paper, a sparse reconstruction by separable approximation algorithm (SpaRSA) is extended to solve the ET inverse problem. The algorithm is competitive with the fastest state-of-the-art algorithms in solving the standard L 2 −L 1 problem. However, it is computationally expensive when the dimension of the matrix is large. To further improve the calculation speed of solving inverse problems, a projection method based on the Krylov subspace is employed and combined with the SpaRSA algorithm. The proposed algorithm is tested with image reconstruction of electrical resistance tomography (ERT). Both simulation and experimental results demonstrate that the proposed method can reduce the computational time and improve the noise robustness for the image reconstruction. (paper)
Noniterative MAP reconstruction using sparse matrix representations.
Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J
We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.
Median prior constrained TV algorithm for sparse view low-dose CT reconstruction.
Liu, Yi; Shangguan, Hong; Zhang, Quan; Zhu, Hongqing; Shu, Huazhong; Gui, Zhiguo
It is known that lowering the X-ray tube current (mAs) or tube voltage (kVp) and simultaneously reducing the total number of X-ray views (sparse view) is an effective means to achieve low-dose in computed tomography (CT) scan. However, the associated image quality by the conventional filtered back-projection (FBP) usually degrades due to the excessive quantum noise. Although sparse-view CT reconstruction algorithm via total variation (TV), in the scanning protocol of reducing X-ray tube current, has been demonstrated to be able to result in significant radiation dose reduction while maintain image quality, noticeable patchy artifacts still exist in reconstructed images. In this study, to address the problem of patchy artifacts, we proposed a median prior constrained TV regularization to retain the image quality by introducing an auxiliary vector m in register with the object. Specifically, the approximate action of m is to draw, in each iteration, an object voxel toward its own local median, aiming to improve low-dose image quality with sparse-view projection measurements. Subsequently, an alternating optimization algorithm is adopted to optimize the associative objective function. We refer to the median prior constrained TV regularization as "TV_MP" for simplicity. Experimental results on digital phantoms and clinical phantom demonstrated that the proposed TV_MP with appropriate control parameters can not only ensure a higher signal to noise ratio (SNR) of the reconstructed image, but also its resolution compared with the original TV method. Copyright © 2015 Elsevier Ltd. All rights reserved.
Demosaicing and Superresolution for Color Filter Array via Residual Image Reconstruction and Sparse Representation
Sun, Guangling
A framework of demosaicing and superresolution for color filter array (CFA) via residual image reconstruction and sparse representation is presented.Given the intermediate image produced by certain demosaicing and interpolation technique, a residual image between the final reconstruction image and the intermediate image is reconstructed using sparse representation.The final reconstruction image has richer edges and details than that of the intermediate image. Specifically, a generic dictionar...
MO-FG-204-08: Optimization-Based Image Reconstruction From Unevenly Distributed Sparse Projection Views
Xie, Huiqiao; Yang, Yi; Tang, Xiangyang; Niu, Tianye; Ren, Yi
Purpose: Optimization-based reconstruction has been proposed and investigated for reconstructing CT images from sparse views, as such the radiation dose can be substantially reduced while maintaining acceptable image quality. The investigation has so far focused on reconstruction from evenly distributed sparse views. Recognizing the clinical situations wherein only unevenly sparse views are available, e.g., image guided radiation therapy, CT perfusion and multi-cycle cardiovascular imaging, we investigate the performance of optimization-based image reconstruction from unevenly sparse projection views in this work. Methods: The investigation is carried out using the FORBILD and an anthropomorphic head phantoms. In the study, 82 views, which are evenly sorted out from a full (360°) axial CT scan consisting of 984 views, form sub-scan I. Another 82 views are sorted out in a similar manner to form sub-scan II. As such, a CT scan with sparse (164) views at 1:6 ratio are formed. By shifting the two sub-scans relatively in view angulation, a CT scan with unevenly distributed sparse (164) views at 1:6 ratio are formed. An optimization-based method is implemented to reconstruct images from the unevenly distributed views. By taking the FBP reconstruction from the full scan (984 views) as the reference, the root mean square (RMS) between the reference and the optimization-based reconstruction is used to evaluate the performance quantitatively. Results: In visual inspection, the optimization-based method outperforms the FBP substantially in the reconstruction from unevenly distributed, which are quantitatively verified by the RMS gauged globally and in ROIs in both the FORBILD and anthropomorphic head phantoms. The RMS increases with increasing severity in the uneven angular distribution, especially in the case of anthropomorphic head phantom. Conclusion: The optimization-based image reconstruction can save radiation dose up to 12-fold while providing acceptable image quality
Bayesian signal reconstruction for 1-bit compressed sensing
Xu, Yingying; Kabashima, Yoshiyuki; Zdeborová, Lenka
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly beneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing and analyze its typical performance using statistical mechanics. As a basic setup, we consider the case that the measuring matrix Φ has i.i.d entries and the measurements y are noiseless. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the l 1 -norm minimization approach, asymptotically saturating the performance obtained when the non-zero entry positions of the signal are known, for signals whose non-zero entries follow zero mean Gaussian distributions. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis. (paper)
A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning.
Zhang, Shang; Dong, Yuhan; Fu, Hongyan; Huang, Shao-Lun; Zhang, Lin
The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer.
A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning
Zhang, Shang; Fu, Hongyan; Huang, Shao-Lun; Zhang, Lin
The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer. PMID:29470406
Compressive Detection Using Sub-Nyquist Radars for Sparse Signals
Ying Sun
Full Text Available This paper investigates the compression detection problem using sub-Nyquist radars, which is well suited to the scenario of high bandwidths in real-time processing because it would significantly reduce the computational burden and save power consumption and computation time. A compressive generalized likelihood ratio test (GLRT detector for sparse signals is proposed for sub-Nyquist radars without ever reconstructing the signal involved. The performance of the compressive GLRT detector is analyzed and the theoretical bounds are presented. The compressive GLRT detection performance of sub-Nyquist radars is also compared to the traditional GLRT detection performance of conventional radars, which employ traditional analog-to-digital conversion (ADC at Nyquist sampling rates. Simulation results demonstrate that the former can perform almost as well as the latter with a very small fraction of the number of measurements required by traditional detection in relatively high signal-to-noise ratio (SNR cases.
Sparse signals recovered by non-convex penalty in quasi-linear systems.
Cui, Angang; Li, Haiyang; Wen, Meng; Peng, Jigen
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is no longer suitable. Compared with the compressed sensing under the linear circumstance, this nonlinear compressed sensing is much more difficult, in fact also NP-hard, combinatorial problem, because of the discrete and discontinuous nature of the [Formula: see text]-norm and the nonlinearity. In order to get a convenience for sparse signal recovery, we set the nonlinear models have a smooth quasi-linear nature in this paper, and study a non-convex fraction function [Formula: see text] in this quasi-linear compressed sensing. We propose an iterative fraction thresholding algorithm to solve the regularization problem [Formula: see text] for all [Formula: see text]. With the change of parameter [Formula: see text], our algorithm could get a promising result, which is one of the advantages for our algorithm compared with some state-of-art algorithms. Numerical experiments show that our method performs much better than some state-of-the-art methods.
Support agnostic Bayesian matching pursuit for block sparse signals
A fast matching pursuit method using a Bayesian approach is introduced for block-sparse signal recovery. This method performs Bayesian estimates of block-sparse signals even when the distribution of active blocks is non-Gaussian or unknown. It is agnostic to the distribution of active blocks in the signal and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data and no user intervention is required. The method requires a priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.
Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction
Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng
Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.
Learning sparse generative models of audiovisual signals
Monaci, Gianluca; Sommer, Friedrich T.; Vandergheynst, Pierre
This paper presents a novel framework to learn sparse represen- tations for audiovisual signals. An audiovisual signal is modeled as a sparse sum of audiovisual kernels. The kernels are bimodal functions made of synchronous audio and video components that can be positioned independently and arbitrarily in space and time. We design an algorithm capable of learning sets of such audiovi- sual, synchronous, shift-invariant functions by alternatingly solving a coding and a learning pr...
Sparse DOA estimation with polynomial rooting
Xenaki, Angeliki; Gerstoft, Peter; Fernandez Grande, Efren
Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve highresol......Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve...... highresolution imaging. Utilizing the dual optimal variables of the CS optimization problem, it is shown with Monte Carlo simulations that the DOAs are accurately reconstructed through polynomial rooting (Root-CS). Polynomial rooting is known to improve the resolution in several other DOA estimation methods...
RMP: Reduced-set matching pursuit approach for efficient compressed sensing signal reconstruction
Michael M. Abdel-Sayed
Full Text Available Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Compressed sensing initially adopted â""1 minimization for signal reconstruction which is computationally expensive. Several greedy recovery algorithms have been recently proposed for signal reconstruction at a lower computational complexity compared to the optimal â""1 minimization, while maintaining a good reconstruction accuracy. In this paper, the Reduced-set Matching Pursuit (RMP greedy recovery algorithm is proposed for compressed sensing. Unlike existing approaches which either select too many or too few values per iteration, RMP aims at selecting the most sufficient number of correlation values per iteration, which improves both the reconstruction time and error. Furthermore, RMP prunes the estimated signal, and hence, excludes the incorrectly selected values. The RMP algorithm achieves a higher reconstruction accuracy at a significantly low computational complexity compared to existing greedy recovery algorithms. It is even superior to â""1 minimization in terms of the normalized time-error product, a new metric introduced to measure the trade-off between the reconstruction time and error. RMP superior performance is illustrated with both noiseless and noisy samples.
RMP: Reduced-set matching pursuit approach for efficient compressed sensing signal reconstruction.
Abdel-Sayed, Michael M; Khattab, Ahmed; Abu-Elyazeed, Mohamed F
Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Compressed sensing initially adopted [Formula: see text] minimization for signal reconstruction which is computationally expensive. Several greedy recovery algorithms have been recently proposed for signal reconstruction at a lower computational complexity compared to the optimal [Formula: see text] minimization, while maintaining a good reconstruction accuracy. In this paper, the Reduced-set Matching Pursuit (RMP) greedy recovery algorithm is proposed for compressed sensing. Unlike existing approaches which either select too many or too few values per iteration, RMP aims at selecting the most sufficient number of correlation values per iteration, which improves both the reconstruction time and error. Furthermore, RMP prunes the estimated signal, and hence, excludes the incorrectly selected values. The RMP algorithm achieves a higher reconstruction accuracy at a significantly low computational complexity compared to existing greedy recovery algorithms. It is even superior to [Formula: see text] minimization in terms of the normalized time-error product, a new metric introduced to measure the trade-off between the reconstruction time and error. RMP superior performance is illustrated with both noiseless and noisy samples.
Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging.
Xingjian Yu
Full Text Available In dynamic Positron Emission Tomography (PET, an estimate of the radio activity concentration is obtained from a series of frames of sinogram data taken at ranging in duration from 10 seconds to minutes under some criteria. So far, all the well-known reconstruction algorithms require known data statistical properties. It limits the speed of data acquisition, besides, it is unable to afford the separated information about the structure and the variation of shape and rate of metabolism which play a major role in improving the visualization of contrast for some requirement of the diagnosing in application. This paper presents a novel low rank-based activity map reconstruction scheme from emission sinograms of dynamic PET, termed as SLCR representing Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging. In this method, the stationary background is formulated as a low rank component while variations between successive frames are abstracted to the sparse. The resulting nuclear norm and l1 norm related minimization problem can also be efficiently solved by many recently developed numerical methods. In this paper, the linearized alternating direction method is applied. The effectiveness of the proposed scheme is illustrated on three data sets.
Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization
Gu, Renliang; Dogandžić, Aleksandar
We propose a method for reconstructing sparse images from polychromatic x-ray computed tomography (ct) measurements via mass attenuation coefficient discretization. The material of the inspected object and the incident spectrum are assumed to be unknown. We rewrite the Lambert-Beer's law in terms of integral expressions of mass attenuation and discretize the resulting integrals. We then present a penalized constrained least-squares optimization approach for reconstructing the underlying object from log-domain measurements, where an active set approach is employed to estimate incident energy density parameters and the nonnegativity and sparsity of the image density map are imposed using negative-energy and smooth ℓ 1 -norm penalty terms. We propose a two-step scheme for refining the mass attenuation discretization grid by using higher sampling rate over the range with higher photon energy, and eliminating the discretization points that have little effect on accuracy of the forward projection model. This refinement allows us to successfully handle the characteristic lines (Dirac impulses) in the incident energy density spectrum. We compare the proposed method with the standard filtered backprojection, which ignores the polychromatic nature of the measurements and sparsity of the image density map. Numerical simulations using both realistic simulated and real x-ray ct data are presented
NUFFT-Based Iterative Image Reconstruction via Alternating Direction Total Variation Minimization for Sparse-View CT
Bin Yan
Full Text Available Sparse-view imaging is a promising scanning method which can reduce the radiation dose in X-ray computed tomography (CT. Reconstruction algorithm for sparse-view imaging system is of significant importance. The adoption of the spatial iterative algorithm for CT image reconstruction has a low operation efficiency and high computation requirement. A novel Fourier-based iterative reconstruction technique that utilizes nonuniform fast Fourier transform is presented in this study along with the advanced total variation (TV regularization for sparse-view CT. Combined with the alternating direction method, the proposed approach shows excellent efficiency and rapid convergence property. Numerical simulations and real data experiments are performed on a parallel beam CT. Experimental results validate that the proposed method has higher computational efficiency and better reconstruction quality than the conventional algorithms, such as simultaneous algebraic reconstruction technique using TV method and the alternating direction total variation minimization approach, with the same time duration. The proposed method appears to have extensive applications in X-ray CT imaging.
Neural Network for Sparse Reconstruction
Qingfa Li
Full Text Available We construct a neural network based on smoothing approximation techniques and projected gradient method to solve a kind of sparse reconstruction problems. Neural network can be implemented by circuits and can be seen as an important method for solving optimization problems, especially large scale problems. Smoothing approximation is an efficient technique for solving nonsmooth optimization problems. We combine these two techniques to overcome the difficulties of the choices of the step size in discrete algorithms and the item in the set-valued map of differential inclusion. In theory, the proposed network can converge to the optimal solution set of the given problem. Furthermore, some numerical experiments show the effectiveness of the proposed network in this paper.
Blind spectrum reconstruction algorithm with L0-sparse representation
Liu, Hai; Zhang, Zhaoli; Liu, Sanyan; Shu, Jiangbo; Liu, Tingting; Zhang, Tianxu
Raman spectrum often suffers from band overlap and Poisson noise. This paper presents a new blind Poissonian Raman spectrum reconstruction method, which incorporates the L 0 -sparse prior together with the total variation constraint into the maximum a posteriori framework. Furthermore, the greedy analysis pursuit algorithm is adopted to solve the L 0 -based minimization problem. Simulated and real spectrum experimental results show that the proposed method can effectively preserve spectral structure and suppress noise. The reconstructed Raman spectra are easily used for interpreting unknown chemical mixtures. (paper)
Robust sparse image reconstruction of radio interferometric observations with PURIFY
Pratley, Luke; McEwen, Jason D.; d'Avezac, Mayeul; Carrillo, Rafael E.; Onose, Alexandru; Wiaux, Yves
Next-generation radio interferometers, such as the Square Kilometre Array, will revolutionize our understanding of the Universe through their unprecedented sensitivity and resolution. However, to realize these goals significant challenges in image and data processing need to be overcome. The standard methods in radio interferometry for reconstructing images, such as CLEAN, have served the community well over the last few decades and have survived largely because they are pragmatic. However, they produce reconstructed interferometric images that are limited in quality and scalability for big data. In this work, we apply and evaluate alternative interferometric reconstruction methods that make use of state-of-the-art sparse image reconstruction algorithms motivated by compressive sensing, which have been implemented in the PURIFY software package. In particular, we implement and apply the proximal alternating direction method of multipliers algorithm presented in a recent article. First, we assess the impact of the interpolation kernel used to perform gridding and degridding on sparse image reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as well as prolate spheroidal wave functions while providing a computational saving and an analytic form. Secondly, we apply PURIFY to real interferometric observations from the Very Large Array and the Australia Telescope Compact Array and find that images recovered by PURIFY are of higher quality than those recovered by CLEAN. Thirdly, we discuss how PURIFY reconstructions exhibit additional advantages over those recovered by CLEAN. The latest version of PURIFY, with developments presented in this work, is made publicly available.
Sparse reconstruction by means of the standard Tikhonov regularization
Lu Shuai; Pereverzev, Sergei V
It is a common belief that Tikhonov scheme with || · ||L 2 -penalty fails in sparse reconstruction. We are going to show, however, that this standard regularization can help if the stability measured in L 1 -norm will be properly taken into account in the choice of the regularization parameter. The crucial point is that now a stability bound may depend on the bases with respect to which the solution of the problem is assumed to be sparse. We discuss how such a stability can be estimated numerically and present the results of computational experiments giving the evidence of the reliability of our approach.
Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner
Yubo Wang
Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.
Wang, Yubo; Veluvolu, Kalyana C
It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Sparse Matrices in Frame Theory
Lemvig, Jakob; Krahmer, Felix; Kutyniok, Gitta
Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames...... yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices...
priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal
Aliasing-free wideband beamforming using sparse signal representation
Tang, Z.; Blacquière, G.; Leus, G.
Sparse signal representation (SSR) is considered to be an appealing alternative to classical beamforming for direction-of-arrival (DOA) estimation. For wideband signals, the SSR-based approach constructs steering matrices, referred to as dictionaries in this paper, corresponding to different
Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization
Jin Zhao; Zhang Han-Ming; Yan Bin; Li Lei; Wang Lin-Yuan; Cai Ai-Long
Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. (paper)
EEG Source Reconstruction using Sparse Basis Function Representations
Hansen, Sofie Therese; Hansen, Lars Kai
-validation this approach is more automated than competing approaches such as Multiple Sparse Priors (Friston et al., 2008) or Champagne (Wipf et al., 2010) that require manual selection of noise level and auxiliary signal free data, respectively. Finally, we propose an unbiased estimator of the reproducibility...
Parametric Human Body Reconstruction Based on Sparse Key Points.
Cheng, Ke-Li; Tong, Ruo-Feng; Tang, Min; Qian, Jing-Ye; Sarkis, Michel
We propose an automatic parametric human body reconstruction algorithm which can efficiently construct a model using a single Kinect sensor. A user needs to stand still in front of the sensor for a couple of seconds to measure the range data. The user's body shape and pose will then be automatically constructed in several seconds. Traditional methods optimize dense correspondences between range data and meshes. In contrast, our proposed scheme relies on sparse key points for the reconstruction. It employs regression to find the corresponding key points between the scanned range data and some annotated training data. We design two kinds of feature descriptors as well as corresponding regression stages to make the regression robust and accurate. Our scheme follows with dense refinement where a pre-factorization method is applied to improve the computational efficiency. Compared with other methods, our scheme achieves similar reconstruction accuracy but significantly reduces runtime.
Accelerated dynamic cardiac MRI exploiting sparse-Kalman-smoother self-calibration and reconstruction (k  −  t SPARKS)
Park, Suhyung; Park, Jaeseok
Accelerated dynamic MRI, which exploits spatiotemporal redundancies in k  −  t space and coil dimension, has been widely used to reduce the number of signal encoding and thus increase imaging efficiency with minimal loss of image quality. Nonetheless, particularly in cardiac MRI it still suffers from artifacts and amplified noise in the presence of time-drifting coil sensitivity due to relative motion between coil and subject (e.g. free breathing). Furthermore, a substantial number of additional calibrating signals is to be acquired to warrant accurate calibration of coil sensitivity. In this work, we propose a novel, accelerated dynamic cardiac MRI with sparse-Kalman-smoother self-calibration and reconstruction (k  −  t SPARKS), which is robust to time-varying coil sensitivity even with a small number of calibrating signals. The proposed k  −  t SPARKS incorporates Kalman-smoother self-calibration in k  −  t space and sparse signal recovery in x  −   f space into a single optimization problem, leading to iterative, joint estimation of time-varying convolution kernels and missing signals in k  −  t space. In the Kalman-smoother calibration, motion-induced uncertainties over the entire time frames were included in modeling state transition while a coil-dependent noise statistic in describing measurement process. The sparse signal recovery iteratively alternates with the self-calibration to tackle the ill-conditioning problem potentially resulting from insufficient calibrating signals. Simulations and experiments were performed using both the proposed and conventional methods for comparison, revealing that the proposed k  −  t SPARKS yields higher signal-to-error ratio and superior temporal fidelity in both breath-hold and free-breathing cardiac applications over all reduction factors. (paper)
Blind compressed sensing image reconstruction based on alternating direction method
Liu, Qinan; Guo, Shuxu
In order to solve the problem of how to reconstruct the original image under the condition of unknown sparse basis, this paper proposes an image reconstruction method based on blind compressed sensing model. In this model, the image signal is regarded as the product of a sparse coefficient matrix and a dictionary matrix. Based on the existing blind compressed sensing theory, the optimal solution is solved by the alternative minimization method. The proposed method solves the problem that the sparse basis in compressed sensing is difficult to represent, which restrains the noise and improves the quality of reconstructed image. This method ensures that the blind compressed sensing theory has a unique solution and can recover the reconstructed original image signal from a complex environment with a stronger self-adaptability. The experimental results show that the image reconstruction algorithm based on blind compressed sensing proposed in this paper can recover high quality image signals under the condition of under-sampling.
Binary Sparse Phase Retrieval via Simulated Annealing
Wei Peng
Full Text Available This paper presents the Simulated Annealing Sparse PhAse Recovery (SASPAR algorithm for reconstructing sparse binary signals from their phaseless magnitudes of the Fourier transform. The greedy strategy version is also proposed for a comparison, which is a parameter-free algorithm. Sufficient numeric simulations indicate that our method is quite effective and suggest the binary model is robust. The SASPAR algorithm seems competitive to the existing methods for its efficiency and high recovery rate even with fewer Fourier measurements.
Real-Space x-ray tomographic reconstruction of randomly oriented objects with sparse data frames.
Ayyer, Kartik; Philipp, Hugh T; Tate, Mark W; Elser, Veit; Gruner, Sol M
Schemes for X-ray imaging single protein molecules using new x-ray sources, like x-ray free electron lasers (XFELs), require processing many frames of data that are obtained by taking temporally short snapshots of identical molecules, each with a random and unknown orientation. Due to the small size of the molecules and short exposure times, average signal levels of much less than 1 photon/pixel/frame are expected, much too low to be processed using standard methods. One approach to process the data is to use statistical methods developed in the EMC algorithm (Loh & Elser, Phys. Rev. E, 2009) which processes the data set as a whole. In this paper we apply this method to a real-space tomographic reconstruction using sparse frames of data (below 10(-2) photons/pixel/frame) obtained by performing x-ray transmission measurements of a low-contrast, randomly-oriented object. This extends the work by Philipp et al. (Optics Express, 2012) to three dimensions and is one step closer to the single molecule reconstruction problem.
Compressed sensing & sparse filtering
Carmi, Avishy Y; Godsill, Simon J
This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary. Apart from compressed sensing this book contains other related app
Noise-aware dictionary-learning-based sparse representation framework for detection and removal of single and combined noises from ECG signal.
Satija, Udit; Ramkumar, Barathram; Sabarimalai Manikandan, M
Automatic electrocardiogram (ECG) signal enhancement has become a crucial pre-processing step in most ECG signal analysis applications. In this Letter, the authors propose an automated noise-aware dictionary learning-based generalised ECG signal enhancement framework which can automatically learn the dictionaries based on the ECG noise type for effective representation of ECG signal and noises, and can reduce the computational load of sparse representation-based ECG enhancement system. The proposed framework consists of noise detection and identification, noise-aware dictionary learning, sparse signal decomposition and reconstruction. The noise detection and identification is performed based on the moving average filter, first-order difference, and temporal features such as number of turning points, maximum absolute amplitude, zerocrossings, and autocorrelation features. The representation dictionary is learned based on the type of noise identified in the previous stage. The proposed framework is evaluated using noise-free and noisy ECG signals. Results demonstrate that the proposed method can significantly reduce computational load as compared with conventional dictionary learning-based ECG denoising approaches. Further, comparative results show that the method outperforms existing methods in automatically removing noises such as baseline wanders, power-line interference, muscle artefacts and their combinations without distorting the morphological content of local waves of ECG signal.
Isotropic 3D cardiac cine MRI allows efficient sparse segmentation strategies based on 3D surface reconstruction.
Odille, Freddy; Bustin, Aurélien; Liu, Shufang; Chen, Bailiang; Vuissoz, Pierre-André; Felblinger, Jacques; Bonnemains, Laurent
Segmentation of cardiac cine MRI data is routinely used for the volumetric analysis of cardiac function. Conventionally, 2D contours are drawn on short-axis (SAX) image stacks with relatively thick slices (typically 8 mm). Here, an acquisition/reconstruction strategy is used for obtaining isotropic 3D cine datasets; reformatted slices are then used to optimize the manual segmentation workflow. Isotropic 3D cine datasets were obtained from multiple 2D cine stacks (acquired during free-breathing in SAX and long-axis (LAX) orientations) using nonrigid motion correction (cine-GRICS method) and super-resolution. Several manual segmentation strategies were then compared, including conventional SAX segmentation, LAX segmentation in three views only, and combinations of SAX and LAX slices. An implicit B-spline surface reconstruction algorithm is proposed to reconstruct the left ventricular cavity surface from the sparse set of 2D contours. All tested sparse segmentation strategies were in good agreement, with Dice scores above 0.9 despite using fewer slices (3-6 sparse slices instead of 8-10 contiguous SAX slices). When compared to independent phase-contrast flow measurements, stroke volumes computed from four or six sparse slices had slightly higher precision than conventional SAX segmentation (error standard deviation of 5.4 mL against 6.1 mL) at the cost of slightly lower accuracy (bias of -1.2 mL against 0.2 mL). Functional parameters also showed a trend to improved precision, including end-diastolic volumes, end-systolic volumes, and ejection fractions). The postprocessing workflow of 3D isotropic cardiac imaging strategies can be optimized using sparse segmentation and 3D surface reconstruction. Magn Reson Med 79:2665-2675, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Recursive nearest neighbor search in a sparse and multiscale domain for comparing audio signals
Sturm, Bob L.; Daudet, Laurent
We investigate recursive nearest neighbor search in a sparse domain at the scale of audio signals. Essentially, to approximate the cosine distance between the signals we make pairwise comparisons between the elements of localized sparse models built from large and redundant multiscale dictionaries...
Analysis Sparse Representation for Nonnegative Signals Based on Determinant Measure by DC Programming
Yujie Li
Full Text Available Analysis sparse representation has recently emerged as an alternative approach to the synthesis sparse model. Most existing algorithms typically employ the l0-norm, which is generally NP-hard. Other existing algorithms employ the l1-norm to relax the l0-norm, which sometimes cannot promote adequate sparsity. Most of these existing algorithms focus on general signals and are not suitable for nonnegative signals. However, many signals are necessarily nonnegative such as spectral data. In this paper, we present a novel and efficient analysis dictionary learning algorithm for nonnegative signals with the determinant-type sparsity measure which is convex and differentiable. The analysis sparse representation can be cast in three subproblems, sparse coding, dictionary update, and signal update, because the determinant-type sparsity measure would result in a complex nonconvex optimization problem, which cannot be easily solved by standard convex optimization methods. Therefore, in the proposed algorithms, we use a difference of convex (DC programming scheme for solving the nonconvex problem. According to our theoretical analysis and simulation study, the main advantage of the proposed algorithm is its greater dictionary learning efficiency, particularly compared with state-of-the-art algorithms. In addition, our proposed algorithm performs well in image denoising.
Fast Estimation of Optimal Sparseness of Music Signals
la Cour-Harbo, Anders
We want to use a variety of sparseness measured applied to 'the minimal L1 norm representation' of a music signal in an overcomplete dictionary as features for automatic classification of music. Unfortunately, the process of computing the optimal L1 norm representation is rather slow, and we...
Interference-Aware OFDM Receiver for Channels with Sparse Common Supports
Barbu, Oana-Elena; Manchón, Carles Navarro; Badiu, Mihai Alin
We design an algorithm for OFDM receivers operating in co-channel interference conditions, where the serving and interfering transmitters are synchronized in time. The channel estimation problem is formulated as one of sparse signal reconstruction using multiple measurement vectors. The proposed...
Quasi Gradient Projection Algorithm for Sparse Reconstruction in Compressed Sensing
Xin Meng
Full Text Available Compressed sensing is a novel signal sampling theory under the condition that the signal is sparse or compressible. The existing recovery algorithms based on the gradient projection can either need prior knowledge or recovery the signal poorly. In this paper, a new algorithm based on gradient projection is proposed, which is referred as Quasi Gradient Projection. The algorithm presented quasi gradient direction and two step sizes schemes along this direction. The algorithm doesn't need any prior knowledge of the original signal. Simulation results demonstrate that the presented algorithm cans recovery the signal more correctly than GPSR which also don't need prior knowledge. Meanwhile, the algorithm has a lower computation complexity.
SD-SEM: sparse-dense correspondence for 3D reconstruction of microscopic samples.
Baghaie, Ahmadreza; Tafti, Ahmad P; Owen, Heather A; D'Souza, Roshan M; Yu, Zeyun
Scanning electron microscopy (SEM) imaging has been a principal component of many studies in biomedical, mechanical, and materials sciences since its emergence. Despite the high resolution of captured images, they remain two-dimensional (2D). In this work, a novel framework using sparse-dense correspondence is introduced and investigated for 3D reconstruction of stereo SEM images. SEM micrographs from microscopic samples are captured by tilting the specimen stage by a known angle. The pair of SEM micrographs is then rectified using sparse scale invariant feature transform (SIFT) features/descriptors and a contrario RANSAC for matching outlier removal to ensure a gross horizontal displacement between corresponding points. This is followed by dense correspondence estimation using dense SIFT descriptors and employing a factor graph representation of the energy minimization functional and loopy belief propagation (LBP) as means of optimization. Given the pixel-by-pixel correspondence and the tilt angle of the specimen stage during the acquisition of micrographs, depth can be recovered. Extensive tests reveal the strength of the proposed method for high-quality reconstruction of microscopic samples. Copyright © 2017 Elsevier Ltd. All rights reserved.
Reconstruction of spatio-temporal temperature from sparse historical records using robust probabilistic principal component regression
Tipton, John; Hooten, Mevin; Goring, Simon
Scientific records of temperature and precipitation have been kept for several hundred years, but for many areas, only a shorter record exists. To understand climate change, there is a need for rigorous statistical reconstructions of the paleoclimate using proxy data. Paleoclimate proxy data are often sparse, noisy, indirect measurements of the climate process of interest, making each proxy uniquely challenging to model statistically. We reconstruct spatially explicit temper...
Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction
Niu, Shanzhou; Yu, Gaohang; Ma, Jianhua; Wang, Jing
Spectral computed tomography (CT) has been a promising technique in research and clinics because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of the different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifact suppression and resolution preservation.
Experimental characterization of the Green's function in a room using sparse reconstruction principles
Fernandez Grande, Efren; Christiansen, Rasmus Ellebæk
Measuring the Green's function over the entire volume of a room would typically require an unfeasible number of measurements, due to requirements on spatial sampling. To alleviate the need for excessive measurements, sparse reconstruction methods can be employed, as they make it possible to recon...
Improving temporal resolution in fMRI using a 3D spiral acquisition and low rank plus sparse (L+S) reconstruction.
Petrov, Andrii Y; Herbst, Michael; Andrew Stenger, V
Rapid whole-brain dynamic Magnetic Resonance Imaging (MRI) is of particular interest in Blood Oxygen Level Dependent (BOLD) functional MRI (fMRI). Faster acquisitions with higher temporal sampling of the BOLD time-course provide several advantages including increased sensitivity in detecting functional activation, the possibility of filtering out physiological noise for improving temporal SNR, and freezing out head motion. Generally, faster acquisitions require undersampling of the data which results in aliasing artifacts in the object domain. A recently developed low-rank (L) plus sparse (S) matrix decomposition model (L+S) is one of the methods that has been introduced to reconstruct images from undersampled dynamic MRI data. The L+S approach assumes that the dynamic MRI data, represented as a space-time matrix M, is a linear superposition of L and S components, where L represents highly spatially and temporally correlated elements, such as the image background, while S captures dynamic information that is sparse in an appropriate transform domain. This suggests that L+S might be suited for undersampled task or slow event-related fMRI acquisitions because the periodic nature of the BOLD signal is sparse in the temporal Fourier transform domain and slowly varying low-rank brain background signals, such as physiological noise and drift, will be predominantly low-rank. In this work, as a proof of concept, we exploit the L+S method for accelerating block-design fMRI using a 3D stack of spirals (SoS) acquisition where undersampling is performed in the k z -t domain. We examined the feasibility of the L+S method to accurately separate temporally correlated brain background information in the L component while capturing periodic BOLD signals in the S component. We present results acquired in control human volunteers at 3T for both retrospective and prospectively acquired fMRI data for a visual activation block-design task. We show that a SoS fMRI acquisition with an
A Unifying model of perfusion and motion applied to reconstruction of sparsely sampled free-breathing myocardial perfusion MRI
Pedersen, Henrik; Ólafsdóttir, Hildur; Larsen, Rasmus
The clinical potential of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is currently limited by respiratory induced motion of the heart. This paper presents a unifying model of perfusion and motion in which respiratory motion becomes an integral part of myocardial perfusion...... quantification. Hence, the need for tedious manual motion correction prior to perfusion quantification is avoided. In addition, we demonstrate that the proposed framework facilitates the process of reconstructing DCEMRI from sparsely sampled data in the presence of respiratory motion. The paper focuses primarily...... on the underlying theory of the proposed framework, but shows in vivo results of respiratory motion correction and simulation results of reconstructing sparsely sampled data....
Quadrature demodulation based circuit implementation of pulse stream for ultrasonic signal FRI sparse sampling
Shoupeng, Song; Zhou, Jiang
Converting ultrasonic signal to ultrasonic pulse stream is the key step of finite rate of innovation (FRI) sparse sampling. At present, ultrasonic pulse-stream-forming techniques are mainly based on digital algorithms. No hardware circuit that can achieve it has been reported. This paper proposes a new quadrature demodulation (QD) based circuit implementation method for forming an ultrasonic pulse stream. Elaborating on FRI sparse sampling theory, the process of ultrasonic signal is explained, followed by a discussion and analysis of ultrasonic pulse-stream-forming methods. In contrast to ultrasonic signal envelope extracting techniques, a quadrature demodulation method (QDM) is proposed. Simulation experiments were performed to determine its performance at various signal-to-noise ratios (SNRs). The circuit was then designed, with mixing module, oscillator, low pass filter (LPF), and root of square sum module. Finally, application experiments were carried out on pipeline sample ultrasonic flaw testing. The experimental results indicate that the QDM can accurately convert ultrasonic signal to ultrasonic pulse stream, and reverse the original signal information, such as pulse width, amplitude, and time of arrival. This technique lays the foundation for ultrasonic signal FRI sparse sampling directly with hardware circuitry. (paper)
Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction
Yang, C L; Wei, H Y; Soleimani, M; Adler, A
Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current–voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results. (paper)
Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.
Yang, C L; Wei, H Y; Adler, A; Soleimani, M
Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.
High resolution depth reconstruction from monocular images and sparse point clouds using deep convolutional neural network
Dimitrievski, Martin; Goossens, Bart; Veelaert, Peter; Philips, Wilfried
Understanding the 3D structure of the environment is advantageous for many tasks in the field of robotics and autonomous vehicles. From the robot's point of view, 3D perception is often formulated as a depth image reconstruction problem. In the literature, dense depth images are often recovered deterministically from stereo image disparities. Other systems use an expensive LiDAR sensor to produce accurate, but semi-sparse depth images. With the advent of deep learning there have also been attempts to estimate depth by only using monocular images. In this paper we combine the best of the two worlds, focusing on a combination of monocular images and low cost LiDAR point clouds. We explore the idea that very sparse depth information accurately captures the global scene structure while variations in image patches can be used to reconstruct local depth to a high resolution. The main contribution of this paper is a supervised learning depth reconstruction system based on a deep convolutional neural network. The network is trained on RGB image patches reinforced with sparse depth information and the output is a depth estimate for each pixel. Using image and point cloud data from the KITTI vision dataset we are able to learn a correspondence between local RGB information and local depth, while at the same time preserving the global scene structure. Our results are evaluated on sequences from the KITTI dataset and our own recordings using a low cost camera and LiDAR setup.
Quantitative Assessment of Variational Surface Reconstruction from Sparse Point Clouds in Freehand 3D Ultrasound Imaging during Image-Guided Tumor Ablation
Shuangcheng Deng
Full Text Available Surface reconstruction for freehand 3D ultrasound is used to provide 3D visualization of a VOI (volume of interest during image-guided tumor ablation surgery. This is a challenge because the recorded 2D B-scans are not only sparse but also non-parallel. To solve this issue, we established a framework to reconstruct the surface of freehand 3D ultrasound imaging in 2011. The key technique for surface reconstruction in that framework is based on variational interpolation presented by Greg Turk for shape transformation and is named Variational Surface Reconstruction (VSR. The main goal of this paper is to evaluate the quality of surface reconstructions, especially when the input data are extremely sparse point clouds from freehand 3D ultrasound imaging, using four methods: Ball Pivoting, Power Crust, Poisson, and VSR. Four experiments are conducted, and quantitative metrics, such as the Hausdorff distance, are introduced for quantitative assessment. The experiment results show that the performance of the proposed VSR method is the best of the four methods at reconstructing surface from sparse data. The VSR method can produce a close approximation to the original surface from as few as two contours, whereas the other three methods fail to do so. The experiment results also illustrate that the reproducibility of the VSR method is the best of the four methods.
The Nonlocal Sparse Reconstruction Algorithm by Similarity Measurement with Shearlet Feature Vector
Wu Qidi
Full Text Available Due to the limited accuracy of conventional methods with image restoration, the paper supplied a nonlocal sparsity reconstruction algorithm with similarity measurement. To improve the performance of restoration results, we proposed two schemes to dictionary learning and sparse coding, respectively. In the part of the dictionary learning, we measured the similarity between patches from degraded image by constructing the Shearlet feature vector. Besides, we classified the patches into different classes with similarity and trained the cluster dictionary for each class, by cascading which we could gain the universal dictionary. In the part of sparse coding, we proposed a novel optimal objective function with the coding residual item, which can suppress the residual between the estimate coding and true sparse coding. Additionally, we show the derivation of self-adaptive regularization parameter in optimization under the Bayesian framework, which can make the performance better. It can be indicated from the experimental results that by taking full advantage of similar local geometric structure feature existing in the nonlocal patches and the coding residual suppression, the proposed method shows advantage both on visual perception and PSNR compared to the conventional methods.
A Sparse Modulation Signal Bispectrum Analysis Method for Rolling Element Bearing Diagnosis
Guangbin Wang
Full Text Available Modulation signal bispectrum (MSB analysis is an effective method to obtain the fault frequency for rolling bearing, but harmonics make fault frequency dense and even frequency aliasing. Carrier frequency of bearing is generally determined by its structure and inherent characteristics and changes with the increase of the damage degree, so it is hard to be accurately found. To solve these problems, this paper proposes a sparse modulation signal bispectrum analysis method. Firstly the vibration signal is demodulated by MSB analysis and its bispectrum is obtained. After the frequency domain filtering, the carrier frequency is computed based on the characteristics of energy concentration at the carrier frequency on MSB. By shift-frequency MSB (SF-MSB, the carrier frequency is moved to the coordinate origin, the entire MSB is shifted for the same distance, and SF-MSB is obtained. At last, the bispectrum is shifted to the frequency zero point and diagonal slices are performed to obtain a sparse representation of MSB. Experimental results show that sparse MSB (S-MSB method can not only eliminate the interference of harmonic frequency, but also make the extracted characteristic frequency of fault more obvious.
Ultra-low dose CT attenuation correction for PET/CT: analysis of sparse view data acquisition and reconstruction algorithms
Rui, Xue; Cheng, Lishui; Long, Yong; Fu, Lin; Alessio, Adam M.; Asma, Evren; Kinahan, Paul E.; De Man, Bruno
For PET/CT systems, PET image reconstruction requires corresponding CT images for anatomical localization and attenuation correction. In the case of PET respiratory gating, multiple gated CT scans can offer phase-matched attenuation and motion correction, at the expense of increased radiation dose. We aim to minimize the dose of the CT scan, while preserving adequate image quality for the purpose of PET attenuation correction by introducing sparse view CT data acquisition. Methods We investigated sparse view CT acquisition protocols resulting in ultra-low dose CT scans designed for PET attenuation correction. We analyzed the tradeoffs between the number of views and the integrated tube current per view for a given dose using CT and PET simulations of a 3D NCAT phantom with lesions inserted into liver and lung. We simulated seven CT acquisition protocols with {984, 328, 123, 41, 24, 12, 8} views per rotation at a gantry speed of 0.35 seconds. One standard dose and four ultra-low dose levels, namely, 0.35 mAs, 0.175 mAs, 0.0875 mAs, and 0.04375 mAs, were investigated. Both the analytical FDK algorithm and the Model Based Iterative Reconstruction (MBIR) algorithm were used for CT image reconstruction. We also evaluated the impact of sinogram interpolation to estimate the missing projection measurements due to sparse view data acquisition. For MBIR, we used a penalized weighted least squares (PWLS) cost function with an approximate total-variation (TV) regularizing penalty function. We compared a tube pulsing mode and a continuous exposure mode for sparse view data acquisition. Global PET ensemble root-mean-squares-error (RMSE) and local ensemble lesion activity error were used as quantitative evaluation metrics for PET image quality. Results With sparse view sampling, it is possible to greatly reduce the CT scan dose when it is primarily used for PET attenuation correction with little or no measureable effect on the PET image. For the four ultra-low dose levels
Sparse linear models: Variational approximate inference and Bayesian experimental design
Seeger, Matthias W
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
Seeger, Matthias W [Saarland University and Max Planck Institute for Informatics, Campus E1.4, 66123 Saarbruecken (Germany)
Fast method of sparse acquisition and reconstruction of view and illumination dependent datasets
Filip, Jiří; Vávra, Radomír
Ro�. 37, �. 5 (2013), s. 376-388 ISSN 0097-8493 R&D Projects: GA ČR GAP103/11/0335 Grant - others:EC ERG (European Reintegration Grant) FP7(BE) 239294 Institutional support: RVO:67985556 Keywords : apparent BRDF * measurement * reconstruction * sparse sampling * portable setup Subject RIV: BD - Theory of Information Impact factor: 1.029, year: 2013 http://library.utia.cas.cz/separaty/2013/RO/filip-0392214.pdf
A new Mumford-Shah total variation minimization based model for sparse-view x-ray computed tomography image reconstruction.
Chen, Bo; Bian, Zhaoying; Zhou, Xiaohui; Chen, Wensheng; Ma, Jianhua; Liang, Zhengrong
Total variation (TV) minimization for the sparse-view x-ray computer tomography (CT) reconstruction has been widely explored to reduce radiation dose. However, due to the piecewise constant assumption for the TV model, the reconstructed images often suffer from over-smoothness on the image edges. To mitigate this drawback of TV minimization, we present a Mumford-Shah total variation (MSTV) minimization algorithm in this paper. The presented MSTV model is derived by integrating TV minimization and Mumford-Shah segmentation. Subsequently, a penalized weighted least-squares (PWLS) scheme with MSTV is developed for the sparse-view CT reconstruction. For simplicity, the proposed algorithm is named as 'PWLS-MSTV.' To evaluate the performance of the present PWLS-MSTV algorithm, both qualitative and quantitative studies were conducted by using a digital XCAT phantom and a physical phantom. Experimental results show that the present PWLS-MSTV algorithm has noticeable gains over the existing algorithms in terms of noise reduction, contrast-to-ratio measure and edge-preservation.
MO-DE-207A-11: Sparse-View CT Reconstruction Via a Novel Non-Local Means Method
Chen, Z; Qi, H; Wu, S; Xu, Y; Zhou, L
Purpose: Sparse-view computed tomography (CT) reconstruction is an effective strategy to reduce the radiation dose delivered to patients. Due to its insufficiency of measurements, traditional non-local means (NLM) based reconstruction methods often lead to over-smoothness in image edges. To address this problem, an adaptive NLM reconstruction method based on rotational invariance (RIANLM) is proposed. Methods: The method consists of four steps: 1) Initializing parameters; 2) Algebraic reconstruction technique (ART) reconstruction using raw projection data; 3) Positivity constraint of the image reconstructed by ART; 4) Update reconstructed image by using RIANLM filtering. In RIANLM, a novel similarity metric that is rotational invariance is proposed and used to calculate the distance between two patches. In this way, any patch with similar structure but different orientation to the reference patch would win a relatively large weight to avoid over-smoothed image. Moreover, the parameter h in RIANLM which controls the decay of the weights is adaptive to avoid over-smoothness, while it in NLM is not adaptive during the whole reconstruction process. The proposed method is named as ART-RIANLM and validated on Shepp-Logan phantom and clinical projection data. Results: In our experiments, the searching neighborhood size is set to 15 by 15 and the similarity window is set to 3 by 3. For the simulated case with a resolution of 256 by 256 Shepp-Logan phantom, the ART-RIANLM produces higher SNR (35.38dB<24.00dB) and lower MAE (0.0006<0.0023) reconstructed image than ART-NLM. The visual inspection demonstrated that the proposed method could suppress artifacts or noises more effectively and preserve image edges better. Similar results were found for clinical data case. Conclusion: A novel ART-RIANLM method for sparse-view CT reconstruction is presented with superior image. Compared to the conventional ART-NLM method, the SNR and MAE from ART-RIANLM increases 47% and decreases 74
Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms.
Liu, Li; Lin, Weikai; Jin, Mingwu
In this paper, we propose two reconstruction algorithms for sparse-view X-ray computed tomography (CT). Treating the reconstruction problems as data fidelity constrained total variation (TV) minimization, both algorithms adapt the alternate two-stage strategy: projection onto convex sets (POCS) for data fidelity and non-negativity constraints and steepest descent for TV minimization. The novelty of this work is to determine iterative parameters automatically from data, thus avoiding tedious manual parameter tuning. In TV minimization, the step sizes of steepest descent are adaptively adjusted according to the difference from POCS update in either the projection domain or the image domain, while the step size of algebraic reconstruction technique (ART) in POCS is determined based on the data noise level. In addition, projection errors are used to compare with the error bound to decide whether to perform ART so as to reduce computational costs. The performance of the proposed methods is studied and evaluated using both simulated and physical phantom data. Our methods with automatic parameter tuning achieve similar, if not better, reconstruction performance compared to a representative two-stage algorithm. Copyright © 2014 Elsevier Ltd. All rights reserved.
Efficient Techniques of Sparse Signal Analysis for Enhanced Recovery of Information in Biomedical Engineering and Geosciences
Sana, Furrukh
Sparse signals are abundant among both natural and man-made signals. Sparsity implies that the signal essentially resides in a small dimensional subspace. The sparsity of the signal can be exploited to improve its recovery from limited and noisy observations. Traditional estimation algorithms generally lack the ability to take advantage of signal sparsity. This dissertation considers several problems in the areas of biomedical engineering and geosciences with the aim of enhancing the recovery of information by exploiting the underlying sparsity in the problem. The objective is to overcome the fundamental bottlenecks, both in terms of estimation accuracies and required computational resources. In the first part of dissertation, we present a high precision technique for the monitoring of human respiratory movements by exploiting the sparsity of wireless ultra-wideband signals. The proposed technique provides a novel methodology of overcoming the Nyquist sampling constraint and enables robust performance in the presence of noise and interferences. We also present a comprehensive framework for the important problem of extracting the fetal electrocardiogram (ECG) signals from abdominal ECG recordings of pregnant women. The multiple measurement vectors approach utilized for this purpose provides an efficient mechanism of exploiting the common structure of ECG signals, when represented in sparse transform domains, and allows leveraging information from multiple ECG electrodes under a joint estimation formulation. In the second part of dissertation, we adopt sparse signal processing principles for improved information recovery in large-scale subsurface reservoir characterization problems. We propose multiple new algorithms for sparse representation of the subsurface geological structures, incorporation of useful prior information in the estimation process, and for reducing computational complexities of the problem. The techniques presented here enable significantly
Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data
Humphries, T.; Winn, J.; Faridani, A.
Recent work in CT image reconstruction has seen increasing interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed heuristic which provides an automatic procedure to 'superiorize' an iterative image reconstruction algorithm with respect to a chosen objective function, such as TV. Under certain conditions, the superiorized algorithm is guaranteed to find a solution that is as satisfactory as any found by the original algorithm with respect to satisfying the constraints of the problem; this solution is also expected to be superior with respect to the chosen objective. Most work on superiorization has used reconstruction algorithms which assume a linear measurement model, which in the case of CT corresponds to data generated from a monoenergetic x-ray beam. Many CT systems generate x-rays from a polyenergetic spectrum, however, in which the measured data represent an integral of object attenuation over all energies in the spectrum. This inconsistency with the linear model produces the well-known beam hardening artifacts, which impair analysis of CT images. In this work we superiorize an iterative algorithm for reconstruction from polyenergetic data, using both TV and an anisotropic TV (ATV) penalty. We apply the superiorized algorithm in numerical phantom experiments modeling both sparse-view and limited-angle scenarios. In our experiments, the superiorized algorithm successfully finds solutions which are as constraints-compatible as those found by the original algorithm, with significantly reduced TV and ATV values. The superiorized algorithm thus produces images with greatly reduced sparse-view and limited angle artifacts, which are also largely free of the beam hardening artifacts that would be present if a superiorized version of a monoenergetic algorithm were used.
Greedy Algorithms for Nonnegativity-Constrained Simultaneous Sparse Recovery
Kim, Daeun; Haldar, Justin P.
This work proposes a family of greedy algorithms to jointly reconstruct a set of vectors that are (i) nonnegative and (ii) simultaneously sparse with a shared support set. The proposed algorithms generalize previous approaches that were designed to impose these constraints individually. Similar to previous greedy algorithms for sparse recovery, the proposed algorithms iteratively identify promising support indices. In contrast to previous approaches, the support index selection procedure has been adapted to prioritize indices that are consistent with both the nonnegativity and shared support constraints. Empirical results demonstrate for the first time that the combined use of simultaneous sparsity and nonnegativity constraints can substantially improve recovery performance relative to existing greedy algorithms that impose less signal structure. PMID:26973368
TH-E-17A-02: High-Pitch and Sparse-View Helical 4D CT Via Iterative Image Reconstruction Method Based On Tensor Framelet
Guo, M; Nam, H; Li, R; Xing, L; Gao, H
Purpose: 4D CT is routinely performed during radiation therapy treatment planning of thoracic and abdominal cancers. Compared with the cine mode, the helical mode is advantageous in temporal resolution. However, a low pitch (∼0.1) for 4D CT imaging is often required instead of the standard pitch (∼1) for static imaging, since standard image reconstruction based on analytic method requires the low-pitch scanning in order to satisfy the data sufficient condition when reconstructing each temporal frame individually. In comparison, the flexible iterative method enables the reconstruction of all temporal frames simultaneously, so that the image similarity among frames can be utilized to possibly perform high-pitch and sparse-view helical 4D CT imaging. The purpose of this work is to investigate such an exciting possibility for faster imaging with lower dose. Methods: A key for highpitch and sparse-view helical 4D CT imaging is the simultaneous reconstruction of all temporal frames using the prior that temporal frames are continuous along the temporal direction. In this work, such a prior is regularized through the sparsity transform based on spatiotemporal tensor framelet (TF) as a multilevel and high-order extension of total variation transform. Moreover, GPU-based fast parallel computing of X-ray transform and its adjoint together with split Bregman method is utilized for solving the 4D image reconstruction problem efficiently and accurately. Results: The simulation studies based on 4D NCAT phantoms were performed with various pitches (i.e., 0.1, 0.2, 0.5, and 1) and sparse views (i.e., 400 views per rotation instead of standard >2000 views per rotation), using 3D iterative individual reconstruction method based on 3D TF and 4D iterative simultaneous reconstruction method based on 4D TF respectively. Conclusion: The proposed TF-based simultaneous 4D image reconstruction method enables high-pitch and sparse-view helical 4D CT with lower dose and faster speed
Sparse representations and compressive sensing for imaging and vision
Patel, Vishal M
Compressed sensing or compressive sensing is a new concept in signal processing where one measures a small number of non-adaptive linear combinations of the signal. These measurements are usually much smaller than the number of samples that define the signal. From these small numbers of measurements, the signal is then reconstructed by non-linear procedure. Compressed sensing has recently emerged as a powerful tool for efficiently processing data in non-traditional ways. In this book, we highlight some of the key mathematical insights underlying sparse representation and compressed sensing and illustrate the role of these theories in classical vision, imaging and biometrics problems.
When sparse coding meets ranking: a joint framework for learning sparse codes and ranking scores
Wang, Jim Jing-Yan
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been considered separately, assuming that data coding and ranking are two independent and irrelevant problems. However, is there any internal relationship between sparse coding and ranking score learning? If yes, how to explore and make use of this internal relationship? In this paper, we try to answer these questions by developing the first joint sparse coding and ranking score learning algorithm. To explore the local distribution in the sparse code space, and also to bridge coding and ranking problems, we assume that in the neighborhood of each data point, the ranking scores can be approximated from the corresponding sparse codes by a local linear function. By considering the local approximation error of ranking scores, the reconstruction error and sparsity of sparse coding, and the query information provided by the user, we construct a unified objective function for learning of sparse codes, the dictionary and ranking scores. We further develop an iterative algorithm to solve this optimization problem.
Online sparse representation for remote sensing compressed-sensed video sampling
Wang, Jie; Liu, Kun; Li, Sheng-liang; Zhang, Li
Most recently, an emerging Compressed Sensing (CS) theory has brought a major breakthrough for data acquisition and recovery. It asserts that a signal, which is highly compressible in a known basis, can be reconstructed with high probability through sampling frequency which is well below Nyquist Sampling Frequency. When applying CS to Remote Sensing (RS) Video imaging, it can directly and efficiently acquire compressed image data by randomly projecting original data to obtain linear and non-adaptive measurements. In this paper, with the help of distributed video coding scheme which is a low-complexity technique for resource limited sensors, the frames of a RS video sequence are divided into Key frames (K frames) and Non-Key frames (CS frames). In other words, the input video sequence consists of many groups of pictures (GOPs) and each GOP consists of one K frame followed by several CS frames. Both of them are measured based on block, but at different sampling rates. In this way, the major encoding computation burden will be shifted to the decoder. At the decoder, the Side Information (SI) is generated for the CS frames using traditional Motion-Compensated Interpolation (MCI) technique according to the reconstructed key frames. The over-complete dictionary is trained by dictionary learning methods based on SI. These learning methods include ICA-like, PCA, K-SVD, MOD, etc. Using these dictionaries, the CS frames could be reconstructed according to sparse-land model. In the numerical experiments, the reconstruction performance of ICA algorithm, which is often evaluated by Peak Signal-to-Noise Ratio (PSNR), has been made compared with other online sparse representation algorithms. The simulation results show its advantages in reducing reconstruction time and robustness in reconstruction performance when applying ICA algorithm to remote sensing video reconstruction.
In Defense of Sparse Tracking: Circulant Sparse Tracker
Zhang, Tianzhu; Bibi, Adel Aamer; Ghanem, Bernard
Sparse representation has been introduced to visual tracking by finding the best target candidate with minimal reconstruction error within the particle filter framework. However, most sparse representation based trackers have high computational cost, less than promising tracking performance, and limited feature representation. To deal with the above issues, we propose a novel circulant sparse tracker (CST), which exploits circulant target templates. Because of the circulant structure property, CST has the following advantages: (1) It can refine and reduce particles using circular shifts of target templates. (2) The optimization can be efficiently solved entirely in the Fourier domain. (3) High dimensional features can be embedded into CST to significantly improve tracking performance without sacrificing much computation time. Both qualitative and quantitative evaluations on challenging benchmark sequences demonstrate that CST performs better than all other sparse trackers and favorably against state-of-the-art methods.
Zhang, Tianzhu
A 3D freehand ultrasound system for multi-view reconstructions from sparse 2D scanning planes.
Yu, Honggang; Pattichis, Marios S; Agurto, Carla; Beth Goens, M
A significant limitation of existing 3D ultrasound systems comes from the fact that the majority of them work with fixed acquisition geometries. As a result, the users have very limited control over the geometry of the 2D scanning planes. We present a low-cost and flexible ultrasound imaging system that integrates several image processing components to allow for 3D reconstructions from limited numbers of 2D image planes and multiple acoustic views. Our approach is based on a 3D freehand ultrasound system that allows users to control the 2D acquisition imaging using conventional 2D probes.For reliable performance, we develop new methods for image segmentation and robust multi-view registration. We first present a new hybrid geometric level-set approach that provides reliable segmentation performance with relatively simple initializations and minimum edge leakage. Optimization of the segmentation model parameters and its effect on performance is carefully discussed. Second, using the segmented images, a new coarse to fine automatic multi-view registration method is introduced. The approach uses a 3D Hotelling transform to initialize an optimization search. Then, the fine scale feature-based registration is performed using a robust, non-linear least squares algorithm. The robustness of the multi-view registration system allows for accurate 3D reconstructions from sparse 2D image planes. Volume measurements from multi-view 3D reconstructions are found to be consistently and significantly more accurate than measurements from single view reconstructions. The volume error of multi-view reconstruction is measured to be less than 5% of the true volume. We show that volume reconstruction accuracy is a function of the total number of 2D image planes and the number of views for calibrated phantom. In clinical in-vivo cardiac experiments, we show that volume estimates of the left ventricle from multi-view reconstructions are found to be in better agreement with clinical
Wang, Jim Jing-Yan; Cui, Xuefeng; Yu, Ge; Guo, Lili; Gao, Xin
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays
A variational EM method for pole-zero modeling of speech with mixed block sparse and Gaussian excitation
Shi, Liming; Nielsen, Jesper Kjær; Jensen, Jesper Rindom
The modeling of speech can be used for speech synthesis and speech recognition. We present a speech analysis method based on pole-zero modeling of speech with mixed block sparse and Gaussian excitation. By using a pole-zero model, instead of the all-pole model, a better spectral fitting can...... be expected. Moreover, motivated by the block sparse glottal flow excitation during voiced speech and the white noise excitation for unvoiced speech, we model the excitation sequence as a combination of block sparse signals and white noise. A variational EM (VEM) method is proposed for estimating...... in reconstructing of the block sparse excitation....
SU-E-I-45: Reconstruction of CT Images From Sparsely-Sampled Data Using the Logarithmic Barrier Method
Xu, H
Purpose: To develop and investigate whether the logarithmic barrier (LB) method can result in high-quality reconstructed CT images using sparsely-sampled noisy projection data Methods: The objective function is typically formulated as the sum of the total variation (TV) and a data fidelity (DF) term with a parameter λ that governs the relative weight between them. Finding the optimized value of λ is a critical step for this approach to give satisfactory results. The proposed LB method avoid using λ by constructing the objective function as the sum of the TV and a log function whose augment is the DF term. Newton's method was used to solve the optimization problem. The algorithm was coded in MatLab2013b. Both Shepp-Logan phantom and a patient lung CT image were used for demonstration of the algorithm. Measured data were simulated by calculating the projection data using radon transform. A Poisson noise model was used to account for the simulated detector noise. The iteration stopped when the difference of the current TV and the previous one was less than 1%. Results: Shepp-Logan phantom reconstruction study shows that filtered back-projection (FBP) gives high streak artifacts for 30 and 40 projections. Although visually the streak artifacts are less pronounced for 64 and 90 projections in FBP, the 1D pixel profiles indicate that FBP gives noisier reconstructed pixel values than LB does. A lung image reconstruction is presented. It shows that use of 64 projections gives satisfactory reconstructed image quality with regard to noise suppression and sharp edge preservation. Conclusion: This study demonstrates that the logarithmic barrier method can be used to reconstruct CT images from sparsely-amped data. The number of projections around 64 gives a balance between the over-smoothing of the sharp demarcation and noise suppression. Future study may extend to CBCT reconstruction and improvement on computation speed
X-ray computed tomography using curvelet sparse regularization.
Wieczorek, Matthias; Frikel, Jürgen; Vogel, Jakob; Eggl, Elena; Kopp, Felix; Noël, Peter B; Pfeiffer, Franz; Demaret, Laurent; Lasser, Tobias
Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography. In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization. Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection. The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.
Reconstruction of sparse connectivity in neural networks from spike train covariances
Pernice, Volker; Rotter, Stefan
The inference of causation from correlation is in general highly problematic. Correspondingly, it is difficult to infer the existence of physical synaptic connections between neurons from correlations in their activity. Covariances in neural spike trains and their relation to network structure have been the subject of intense research, both experimentally and theoretically. The influence of recurrent connections on covariances can be characterized directly in linear models, where connectivity in the network is described by a matrix of linear coupling kernels. However, as indirect connections also give rise to covariances, the inverse problem of inferring network structure from covariances can generally not be solved unambiguously. Here we study to what degree this ambiguity can be resolved if the sparseness of neural networks is taken into account. To reconstruct a sparse network, we determine the minimal set of linear couplings consistent with the measured covariances by minimizing the L 1 norm of the coupling matrix under appropriate constraints. Contrary to intuition, after stochastic optimization of the coupling matrix, the resulting estimate of the underlying network is directed, despite the fact that a symmetric matrix of count covariances is used for inference. The performance of the new method is best if connections are neither exceedingly sparse, nor too dense, and it is easily applicable for networks of a few hundred nodes. Full coupling kernels can be obtained from the matrix of full covariance functions. We apply our method to networks of leaky integrate-and-fire neurons in an asynchronous–irregular state, where spike train covariances are well described by a linear model. (paper)
Noise reduction by sparse representation in learned dictionaries for application to blind tip reconstruction problem
Jóźwiak, Grzegorz
Scanning probe microscopy (SPM) is a well known tool used for the investigation of phenomena in objects in the nanometer size range. However, quantitative results are limited by the size and the shape of the nanoprobe used in experiments. Blind tip reconstruction (BTR) is a very popular method used to reconstruct the upper boundary on the shape of the probe. This method is known to be very sensitive to all kinds of interference in the atomic force microscopy (AFM) image. Due to mathematical morphology calculus, the interference makes the BTR results biased rather than randomly disrupted. For this reason, the careful choice of methods used for image enhancement and denoising, as well as the shape of a calibration sample are very important. In the paper, the results of thorough investigations on the shape of a calibration standard are shown. A novel shape is proposed and a tool for the simulation of AFM images of this calibration standard was designed. It was shown that careful choice of the initial tip allows us to use images of hole structures to blindly reconstruct the shape of a probe. The simulator was used to test the impact of modern filtration algorithms on the BTR process. These techniques are based on sparse approximation with function dictionaries learned on the basis of an image itself. Various learning algorithms and parameters were tested to determine the optimal combination for sparse representation. It was observed that the strong reduction of noise does not guarantee strong reduction in reconstruction errors. It seems that further improvements will be possible by the combination of BTR and a noise reduction procedure. (paper)
Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.
He, Xiaowei; Liang, Jimin; Wang, Xiaorui; Yu, Jingjing; Qu, Xiaochao; Wang, Xiaodong; Hou, Yanbin; Chen, Duofang; Liu, Fang; Tian, Jie
In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (â""1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.
Multi-linear sparse reconstruction for SAR imaging based on higher-order SVD
Gao, Yu-Fei; Gui, Guan; Cong, Xun-Chao; Yang, Yue; Zou, Yan-Bin; Wan, Qun
This paper focuses on the spotlight synthetic aperture radar (SAR) imaging for point scattering targets based on tensor modeling. In a real-world scenario, scatterers usually distribute in the block sparse pattern. Such a distribution feature has been scarcely utilized by the previous studies of SAR imaging. Our work takes advantage of this structure property of the target scene, constructing a multi-linear sparse reconstruction algorithm for SAR imaging. The multi-linear block sparsity is introduced into higher-order singular value decomposition (SVD) with a dictionary constructing procedure by this research. The simulation experiments for ideal point targets show the robustness of the proposed algorithm to the noise and sidelobe disturbance which always influence the imaging quality of the conventional methods. The computational resources requirement is further investigated in this paper. As a consequence of the algorithm complexity analysis, the present method possesses the superiority on resource consumption compared with the classic matching pursuit method. The imaging implementations for practical measured data also demonstrate the effectiveness of the algorithm developed in this paper.
Supervised Convolutional Sparse Coding
Affara, Lama Ahmed
Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional sparse coding, which aims at learning discriminative dictionaries instead of purely reconstructive ones. We incorporate a supervised regularization term into the traditional unsupervised CSC objective to encourage the final dictionary elements to be discriminative. Experimental results show that using supervised convolutional learning results in two key advantages. First, we learn more semantically relevant filters in the dictionary and second, we achieve improved image reconstruction on unseen data.
Sparse Image Reconstruction on the Sphere: Analysis and Synthesis.
Wallis, Christopher G R; Wiaux, Yves; McEwen, Jason D
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising, inpainting, and deconvolution problems and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l 1 norm appearing in the regularization problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353-GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.
Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals
Cho, Myung
We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.
Cho, Myung; Cai, Jian-Feng; Liu, Suhui; Eldar, Yonina C.; Xu, Weiyu
Liquid Argon TPC Signal Formation, Signal Processing and Hit Reconstruction
Baller, Bruce [Fermilab
This document describes the early stage of the reconstruction chain that was developed for the ArgoNeuT and MicroBooNE experiments at Fermilab. These experiments study accelerator neutrino interactions that occur in a Liquid Argon Time Projection Chamber. Reconstructing the properties of particles produced in these interactions requires knowledge of the micro-physics processes that affect the creation and transport of ionization electrons to the readout system. A wire signal deconvolution technique was developed to convert wire signals to a standard form for hit reconstruction, to remove artifacts in the electronics chain and to remove coherent noise.
Low-dose X-ray computed tomography image reconstruction with a combined low-mAs and sparse-view protocol.
Gao, Yang; Bian, Zhaoying; Huang, Jing; Zhang, Yunwan; Niu, Shanzhou; Feng, Qianjin; Chen, Wufan; Liang, Zhengrong; Ma, Jianhua
To realize low-dose imaging in X-ray computed tomography (CT) examination, lowering milliampere-seconds (low-mAs) or reducing the required number of projection views (sparse-view) per rotation around the body has been widely studied as an easy and effective approach. In this study, we are focusing on low-dose CT image reconstruction from the sinograms acquired with a combined low-mAs and sparse-view protocol and propose a two-step image reconstruction strategy. Specifically, to suppress significant statistical noise in the noisy and insufficient sinograms, an adaptive sinogram restoration (ASR) method is first proposed with consideration of the statistical property of sinogram data, and then to further acquire a high-quality image, a total variation based projection onto convex sets (TV-POCS) method is adopted with a slight modification. For simplicity, the present reconstruction strategy was termed as "ASR-TV-POCS." To evaluate the present ASR-TV-POCS method, both qualitative and quantitative studies were performed on a physical phantom. Experimental results have demonstrated that the present ASR-TV-POCS method can achieve promising gains over other existing methods in terms of the noise reduction, contrast-to-noise ratio, and edge detail preservation.
Source Signals Separation and Reconstruction Following Principal Component Analysis
WANG Cheng
Full Text Available For separation and reconstruction of source signals from observed signals problem, the physical significance of blind source separation modal and independent component analysis is not very clear, and its solution is not unique. Aiming at these disadvantages, a new linear and instantaneous mixing model and a novel source signals separation reconstruction solving method from observed signals based on principal component analysis (PCA are put forward. Assumption of this new model is statistically unrelated rather than independent of source signals, which is different from the traditional blind source separation model. A one-to-one relationship between linear and instantaneous mixing matrix of new model and linear compound matrix of PCA, and a one-to-one relationship between unrelated source signals and principal components are demonstrated using the concept of linear separation matrix and unrelated of source signals. Based on this theoretical link, source signals separation and reconstruction problem is changed into PCA of observed signals then. The theoretical derivation and numerical simulation results show that, in despite of Gauss measurement noise, wave form and amplitude information of unrelated source signal can be separated and reconstructed by PCA when linear mixing matrix is column orthogonal and normalized; only wave form information of unrelated source signal can be separated and reconstructed by PCA when linear mixing matrix is column orthogonal but not normalized, unrelated source signal cannot be separated and reconstructed by PCA when mixing matrix is not column orthogonal or linear.
Compressing Sensing Based Source Localization for Controlled Acoustic Signals Using Distributed Microphone Arrays
Wei Ke
Full Text Available In order to enhance the accuracy of sound source localization in noisy and reverberant environments, this paper proposes an adaptive sound source localization method based on distributed microphone arrays. Since sound sources lie at a few points in the discrete spatial domain, our method can exploit this inherent sparsity to convert the localization problem into a sparse recovery problem based on the compressive sensing (CS theory. In this method, a two-step discrete cosine transform- (DCT- based feature extraction approach is utilized to cover both short-time and long-time properties of acoustic signals and reduce the dimensions of the sparse model. In addition, an online dictionary learning (DL method is used to adjust the dictionary for matching the changes of audio signals, and then the sparse solution could better represent location estimations. Moreover, we propose an improved block-sparse reconstruction algorithm using approximate l0 norm minimization to enhance reconstruction performance for sparse signals in low signal-noise ratio (SNR conditions. The effectiveness of the proposed scheme is demonstrated by simulation results and experimental results where substantial improvement for localization performance can be obtained in the noisy and reverberant conditions.
Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT
Daniel ePotts
Full Text Available In spectral estimation, one has to determine all parameters of an exponential sum for finitely many (noisysampled data of this exponential sum.Frequently used methods for spectral estimation are MUSIC (MUltiple SIgnal Classification and ESPRIT (Estimation of Signal Parameters viaRotational Invariance Technique.For a trigonometric polynomial of large sparsity, we present a new sparse fast Fourier transform byshifted sampling and using MUSIC resp. ESPRIT, where the ESPRIT based method has lower computational cost.Later this technique is extended to a new reconstruction of a multivariate trigonometric polynomial of large sparsity for given (noisy values sampled on a reconstructing rank-1 lattice. Numerical experiments illustrate thehigh performance of these procedures.
Structural Sparse Tracking
Sparse representation has been applied to visual tracking by finding the best target candidate with minimal reconstruction error by use of target templates. However, most sparse representation based trackers only consider holistic or local representations and do not make full use of the intrinsic structure among and inside target candidates, thereby making the representation less effective when similar objects appear or under occlusion. In this paper, we propose a novel Structural Sparse Tracking (SST) algorithm, which not only exploits the intrinsic relationship among target candidates and their local patches to learn their sparse representations jointly, but also preserves the spatial layout structure among the local patches inside each target candidate. We show that our SST algorithm accommodates most existing sparse trackers with the respective merits. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed SST algorithm performs favorably against several state-of-the-art methods.
Xu, H [Department of Radiation Oncology, Dalhousie University, Halifax, NS (Canada)
Purpose: To develop and investigate whether the logarithmic barrier (LB) method can result in high-quality reconstructed CT images using sparsely-sampled noisy projection data Methods: The objective function is typically formulated as the sum of the total variation (TV) and a data fidelity (DF) term with a parameter λ that governs the relative weight between them. Finding the optimized value of λ is a critical step for this approach to give satisfactory results. The proposed LB method avoid using λ by constructing the objective function as the sum of the TV and a log function whose augment is the DF term. Newton's method was used to solve the optimization problem. The algorithm was coded in MatLab2013b. Both Shepp-Logan phantom and a patient lung CT image were used for demonstration of the algorithm. Measured data were simulated by calculating the projection data using radon transform. A Poisson noise model was used to account for the simulated detector noise. The iteration stopped when the difference of the current TV and the previous one was less than 1%. Results: Shepp-Logan phantom reconstruction study shows that filtered back-projection (FBP) gives high streak artifacts for 30 and 40 projections. Although visually the streak artifacts are less pronounced for 64 and 90 projections in FBP, the 1D pixel profiles indicate that FBP gives noisier reconstructed pixel values than LB does. A lung image reconstruction is presented. It shows that use of 64 projections gives satisfactory reconstructed image quality with regard to noise suppression and sharp edge preservation. Conclusion: This study demonstrates that the logarithmic barrier method can be used to reconstruct CT images from sparsely-amped data. The number of projections around 64 gives a balance between the over-smoothing of the sharp demarcation and noise suppression. Future study may extend to CBCT reconstruction and improvement on computation speed.
Liquid argon TPC signal formation, signal processing and reconstruction techniques
Baller, B.
This document describes a reconstruction chain that was developed for the ArgoNeuT and MicroBooNE experiments at Fermilab. These experiments study accelerator neutrino interactions that occur in a Liquid Argon Time Projection Chamber. Reconstructing the properties of particles produced in these interactions benefits from the knowledge of the micro-physics processes that affect the creation and transport of ionization electrons to the readout system. A wire signal deconvolution technique was developed to convert wire signals to a standard form for hit reconstruction, to remove artifacts in the electronics chain and to remove coherent noise. A unique clustering algorithm reconstructs line-like trajectories and vertices in two dimensions which are then matched to create of 3D objects. These techniques and algorithms are available to all experiments that use the LArSoft suite of software.
An Online Full-Body Motion Recognition Method Using Sparse and Deficient Signal Sequences
Chengyu Guo
Full Text Available This paper presents a method to recognize continuous full-body human motion online by using sparse, low-cost sensors. The only input signals needed are linear accelerations without any rotation information, which are provided by four Wiimote sensors attached to the four human limbs. Based on the fused hidden Markov model (FHMM and autoregressive process, a predictive fusion model (PFM is put forward, which considers the different influences of the upper and lower limbs, establishes HMM for each part, and fuses them using a probabilistic fusion model. Then an autoregressive process is introduced in HMM to predict the gesture, which enables the model to deal with incomplete signal data. In order to reduce the number of alternatives in the online recognition process, a graph model is built that rejects parts of motion types based on the graph structure and previous recognition results. Finally, an online signal segmentation method based on semantics information and PFM is presented to finish the efficient recognition task. The results indicate that the method is robust with a high recognition rate of sparse and deficient signals and can be used in various interactive applications.
Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging.
Yunsong Liu
Full Text Available Compressed sensing has shown to be promising to accelerate magnetic resonance imaging. In this new technology, magnetic resonance images are usually reconstructed by enforcing its sparsity in sparse image reconstruction models, including both synthesis and analysis models. The synthesis model assumes that an image is a sparse combination of atom signals while the analysis model assumes that an image is sparse after the application of an analysis operator. Balanced model is a new sparse model that bridges analysis and synthesis models by introducing a penalty term on the distance of frame coefficients to the range of the analysis operator. In this paper, we study the performance of the balanced model in tight frame based compressed sensing magnetic resonance imaging and propose a new efficient numerical algorithm to solve the optimization problem. By tuning the balancing parameter, the new model achieves solutions of three models. It is found that the balanced model has a comparable performance with the analysis model. Besides, both of them achieve better results than the synthesis model no matter what value the balancing parameter is. Experiment shows that our proposed numerical algorithm constrained split augmented Lagrangian shrinkage algorithm for balanced model (C-SALSA-B converges faster than previously proposed algorithms accelerated proximal algorithm (APG and alternating directional method of multipliers for balanced model (ADMM-B.
Sparse spectral deconvolution algorithm for noncartesian MR spectroscopic imaging.
Bhave, Sampada; Eslami, Ramin; Jacob, Mathews
To minimize line shape distortions and spectral leakage artifacts in MR spectroscopic imaging (MRSI). A spatially and spectrally regularized non-Cartesian MRSI algorithm that uses the line shape distortion priors, estimated from water reference data, to deconvolve the spectra is introduced. Sparse spectral regularization is used to minimize noise amplification associated with deconvolution. A spiral MRSI sequence that heavily oversamples the central k-space regions is used to acquire the MRSI data. The spatial regularization term uses the spatial supports of brain and extracranial fat regions to recover the metabolite spectra and nuisance signals at two different resolutions. Specifically, the nuisance signals are recovered at the maximum resolution to minimize spectral leakage, while the point spread functions of metabolites are controlled to obtain acceptable signal-to-noise ratio. The comparisons of the algorithm against Tikhonov regularized reconstructions demonstrates considerably reduced line-shape distortions and improved metabolite maps. The proposed sparsity constrained spectral deconvolution scheme is effective in minimizing the line-shape distortions. The dual resolution reconstruction scheme is capable of minimizing spectral leakage artifacts. Copyright © 2013 Wiley Periodicals, Inc.
Reconstruction of periodic signals using neural networks
José Danilo Rairán Antolines
Full Text Available In this paper, we reconstruct a periodic signal by using two neural networks. The first network is trained to approximate the period of a signal, and the second network estimates the corresponding coefficients of the signal's Fourier expansion. The reconstruction strategy consists in minimizing the mean-square error via backpro-pagation algorithms over a single neuron with a sine transfer function. Additionally, this paper presents mathematical proof about the quality of the approximation as well as a first modification of the algorithm, which requires less data to reach the same estimation; thus making the algorithm suitable for real-time implementations.
Multifractal signal reconstruction based on singularity power spectrum
Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning
Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.
Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization
Parekh, Ankit
Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the â""1 norm is used to induce sparsity, so much so that â""1 regularization is considered to be `modern least-squares'. The use of â""1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the â""1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal
Bayesian Inference Methods for Sparse Channel Estimation
Pedersen, Niels Lovmand
This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...
High Order Tensor Formulation for Convolutional Sparse Coding
Bibi, Adel Aamer
Convolutional sparse coding (CSC) has gained attention for its successful role as a reconstruction and a classification tool in the computer vision and machine learning community. Current CSC methods can only reconstruct singlefeature 2D images independently. However, learning multidimensional dictionaries and sparse codes for the reconstruction of multi-dimensional data is very important, as it examines correlations among all the data jointly. This provides more capacity for the learned dictionaries to better reconstruct data. In this paper, we propose a generic and novel formulation for the CSC problem that can handle an arbitrary order tensor of data. Backed with experimental results, our proposed formulation can not only tackle applications that are not possible with standard CSC solvers, including colored video reconstruction (5D- tensors), but it also performs favorably in reconstruction with much fewer parameters as compared to naive extensions of standard CSC to multiple features/channels.
Speech Denoising in White Noise Based on Signal Subspace Low-rank Plus Sparse Decomposition
yuan Shuai
Full Text Available In this paper, a new subspace speech enhancement method using low-rank and sparse decomposition is presented. In the proposed method, we firstly structure the corrupted data as a Toeplitz matrix and estimate its effective rank for the underlying human speech signal. Then the low-rank and sparse decomposition is performed with the guidance of speech rank value to remove the noise. Extensive experiments have been carried out in white Gaussian noise condition, and experimental results show the proposed method performs better than conventional speech enhancement methods, in terms of yielding less residual noise and lower speech distortion.
Confidence of model based shape reconstruction from sparse data
Baka, N.; de Bruijne, Marleen; Reiber, J. H. C.
Statistical shape models (SSM) are commonly applied for plausible interpolation of missing data in medical imaging. However, when fitting a shape model to sparse information, many solutions may fit the available data. In this paper we derive a constrained SSM to fit noisy sparse input landmarks...
Towards the low-dose characterization of beam sensitive nanostructures via implementation of sparse image acquisition in scanning transmission electron microscopy
Hwang, Sunghwan; Han, Chang Wan; Ortalan, Volkan; Venkatakrishnan, Singanallur V; Bouman, Charles A
Scanning transmission electron microscopy (STEM) has been successfully utilized to investigate atomic structure and chemistry of materials with atomic resolution. However, STEM's focused electron probe with a high current density causes the electron beam damages including radiolysis and knock-on damage when the focused probe is exposed onto the electron-beam sensitive materials. Therefore, it is highly desirable to decrease the electron dose used in STEM for the investigation of biological/organic molecules, soft materials and nanomaterials in general. With the recent emergence of novel sparse signal processing theories, such as compressive sensing and model-based iterative reconstruction, possibilities of operating STEM under a sparse acquisition scheme to reduce the electron dose have been opened up. In this paper, we report our recent approach to implement a sparse acquisition in STEM mode executed by a random sparse-scan and a signal processing algorithm called model-based iterative reconstruction (MBIR). In this method, a small portion, such as 5% of randomly chosen unit sampling areas (i.e. electron probe positions), which corresponds to pixels of a STEM image, within the region of interest (ROI) of the specimen are scanned with an electron probe to obtain a sparse image. Sparse images are then reconstructed using the MBIR inpainting algorithm to produce an image of the specimen at the original resolution that is consistent with an image obtained using conventional scanning methods. Experimental results for down to 5% sampling show consistency with the full STEM image acquired by the conventional scanning method. Although, practical limitations of the conventional STEM instruments, such as internal delays of the STEM control electronics and the continuous electron gun emission, currently hinder to achieve the full potential of the sparse acquisition STEM in realizing the low dose imaging condition required for the investigation of beam-sensitive materials
Performance Comparison of Reconstruction Algorithms in Discrete Blind Multi-Coset Sampling
Grigoryan, Ruben; Arildsen, Thomas; Tandur, Deepaknath
This paper investigates the performance of different reconstruction algorithms in discrete blind multi-coset sampling. Multi-coset scheme is a promising compressed sensing architecture that can replace traditional Nyquist-rate sampling in the applications with multi-band frequency sparse signals...
Reconstruction of chaotic signals with applications to chaos-based communications
Feng, Jiu Chao
This book provides a systematic review of the fundamental theory of signal reconstruction and the practical techniques used in reconstructing chaotic signals. Specific applications of signal reconstruction methods in chaos-based communications are expounded in full detail, along with examples illustrating the various problems associated with such applications.The book serves as an advanced textbook for undergraduate and graduate courses in electronic and information engineering, automatic control, physics and applied mathematics. It is also highly suited for general nonlinear scientists who wi
Resonance-Based Sparse Signal Decomposition and its Application in Mechanical Fault Diagnosis: A Review.
Huang, Wentao; Sun, Hongjian; Wang, Weijie
Mechanical equipment is the heart of industry. For this reason, mechanical fault diagnosis has drawn considerable attention. In terms of the rich information hidden in fault vibration signals, the processing and analysis techniques of vibration signals have become a crucial research issue in the field of mechanical fault diagnosis. Based on the theory of sparse decomposition, Selesnick proposed a novel nonlinear signal processing method: resonance-based sparse signal decomposition (RSSD). Since being put forward, RSSD has become widely recognized, and many RSSD-based methods have been developed to guide mechanical fault diagnosis. This paper attempts to summarize and review the theoretical developments and application advances of RSSD in mechanical fault diagnosis, and to provide a more comprehensive reference for those interested in RSSD and mechanical fault diagnosis. Followed by a brief introduction of RSSD's theoretical foundation, based on different optimization directions, applications of RSSD in mechanical fault diagnosis are categorized into five aspects: original RSSD, parameter optimized RSSD, subband optimized RSSD, integrated optimized RSSD, and RSSD combined with other methods. On this basis, outstanding issues in current RSSD study are also pointed out, as well as corresponding instructional solutions. We hope this review will provide an insightful reference for researchers and readers who are interested in RSSD and mechanical fault diagnosis.
Signal Recovery in Compressive Sensing via Multiple Sparsifying Bases
Wijewardhana, U. L.; Belyaev, Evgeny; Codreanu, M.
is sparse is the key assumption utilized by such algorithms. However, the basis in which the signal is the sparsest is unknown for many natural signals of interest. Instead there may exist multiple bases which lead to a compressible representation of the signal: e.g., an image is compressible in different...... wavelet transforms. We show that a significant performance improvement can be achieved by utilizing multiple estimates of the signal using sparsifying bases in the context of signal reconstruction from compressive samples. Further, we derive a customized interior-point method to jointly obtain multiple...... estimates of a 2-D signal (image) from compressive measurements utilizing multiple sparsifying bases as well as the fact that the images usually have a sparse gradient....
Reducing the Computational Complexity of Reconstruction in Compressed Sensing Nonuniform Sampling
Grigoryan, Ruben; Jensen, Tobias Lindstrøm; Arildsen, Thomas
sparse signals, but requires computationally expensive reconstruction algorithms. This can be an obstacle for real-time applications. The reduction of complexity is achieved by applying a multi-coset sampling procedure. This proposed method reduces the size of the dictionary matrix, the size...
Accurate signal reconstruction for higher order Lagrangian–Eulerian back-coupling in multiphase turbulence
Zwick, D; Balachandar, S [Department of Mechanical and Aerospace Engineering, University of Florida, FL, United States of America (United States); Sakhaee, E; Entezari, A, E-mail: dpzwick@ufl.edu [Department of Computer and Information Science and Engineering, University of Florida, FL, United States of America (United States)
Multiphase flow simulation serves a vital purpose in applications as diverse as engineering design, natural disaster prediction, and even study of astrophysical phenomena. In these scenarios, it can be very difficult, expensive, or even impossible to fully represent the physical system under consideration. Even still, many such real-world applications can be modeled as a two-phase flow containing both continuous and dispersed phases. Consequentially, the continuous phase is thought of as a fluid and the dispersed phase as particles. The continuous phase is typically treated in the Eulerian frame of reference and represented on a fixed grid, while the dispersed phase is treated in the Lagrangian frame and represented by a sample distribution of Lagrangian particles that approximate a cloud. Coupling between the phases requires interpolation of the continuous phase properties at the locations of the Lagrangian particles. This interpolation step is straightforward and can be performed at higher order accuracy. The reverse process of projecting the Lagrangian particle properties from the sample points to the Eulerian grid is complicated by the time-dependent non-uniform distribution of the Lagrangian particles. In this paper we numerically examine three reconstruction, or projection, methods: (i) direct summation (DS), (ii) least-squares, and (iii) sparse approximation. We choose a continuous representation of the dispersed phase property that is systematically varied from a simple single mode periodic signal to a more complex artificially constructed turbulent signal to see how each method performs in reconstruction. In these experiments, we show that there is a link between the number of dispersed Lagrangian sample points and the number of structured grid points to accurately represent the underlying functional representation to machine accuracy. The least-squares method outperforms the other methods in most cases, while the sparse approximation method is able to
Reconstruction of ECG signals in presence of corruption.
Ganeshapillai, Gartheeban; Liu, Jessica F; Guttag, John
We present an approach to identifying and reconstructing corrupted regions in a multi-parameter physiological signal. The method, which uses information in correlated signals, is specifically designed to preserve clinically significant aspects of the signals. We use template matching to jointly segment the multi-parameter signal, morphological dissimilarity to estimate the quality of the signal segment, similarity search using features on a database of templates to find the closest match, and time-warping to reconstruct the corrupted segment with the matching template. In experiments carried out on the MIT-BIH Arrhythmia Database, a two-parameter database with many clinically significant arrhythmias, our method improved the classification accuracy of the beat type by more than 7 times on a signal corrupted with white Gaussian noise, and increased the similarity to the original signal, as measured by the normalized residual distance, by more than 2.5 times.
Bibi, Adel Aamer; Ghanem, Bernard
Convolutional sparse coding (CSC) has gained attention for its successful role as a reconstruction and a classification tool in the computer vision and machine learning community. Current CSC methods can only reconstruct singlefeature 2D images
Receiver-based recovery of clipped ofdm signals for papr reduction: A bayesian approach
Ali, Anum
Clipping is one of the simplest peak-to-average power ratio reduction schemes for orthogonal frequency division multiplexing (OFDM). Deliberately clipping the transmission signal degrades system performance, and clipping mitigation is required at the receiver for information restoration. In this paper, we acknowledge the sparse nature of the clipping signal and propose a low-complexity Bayesian clipping estimation scheme. The proposed scheme utilizes a priori information about the sparsity rate and noise variance for enhanced recovery. At the same time, the proposed scheme is robust against inaccurate estimates of the clipping signal statistics. The undistorted phase property of the clipped signal, as well as the clipping likelihood, is utilized for enhanced reconstruction. Furthermore, motivated by the nature of modern OFDM-based communication systems, we extend our clipping reconstruction approach to multiple antenna receivers and multi-user OFDM.We also address the problem of channel estimation from pilots contaminated by the clipping distortion. Numerical findings are presented that depict favorable results for the proposed scheme compared to the established sparse reconstruction schemes.
Optimization and validation of accelerated golden-angle radial sparse MRI reconstruction with self-calibrating GRAPPA operator gridding.
Benkert, Thomas; Tian, Ye; Huang, Chenchan; DiBella, Edward V R; Chandarana, Hersh; Feng, Li
Golden-angle radial sparse parallel (GRASP) MRI reconstruction requires gridding and regridding to transform data between radial and Cartesian k-space. These operations are repeatedly performed in each iteration, which makes the reconstruction computationally demanding. This work aimed to accelerate GRASP reconstruction using self-calibrating GRAPPA operator gridding (GROG) and to validate its performance in clinical imaging. GROG is an alternative gridding approach based on parallel imaging, in which k-space data acquired on a non-Cartesian grid are shifted onto a Cartesian k-space grid using information from multicoil arrays. For iterative non-Cartesian image reconstruction, GROG is performed only once as a preprocessing step. Therefore, the subsequent iterative reconstruction can be performed directly in Cartesian space, which significantly reduces computational burden. Here, a framework combining GROG with GRASP (GROG-GRASP) is first optimized and then compared with standard GRASP reconstruction in 22 prostate patients. GROG-GRASP achieved approximately 4.2-fold reduction in reconstruction time compared with GRASP (∼333 min versus ∼78 min) while maintaining image quality (structural similarity index ≈ 0.97 and root mean square error ≈ 0.007). Visual image quality assessment by two experienced radiologists did not show significant differences between the two reconstruction schemes. With a graphics processing unit implementation, image reconstruction time can be further reduced to approximately 14 min. The GRASP reconstruction can be substantially accelerated using GROG. This framework is promising toward broader clinical application of GRASP and other iterative non-Cartesian reconstruction methods. Magn Reson Med 80:286-293, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Sparse image representation for jet neutron and gamma tomography
Craciunescu, T. [EURATOM-MEdC Association, Institute for Laser, Plasma and Radiation Physics, Bucharest (Romania); Kiptily, V. [EURATOM/CCFE Association, Culham Science Centre, Abingdon (United Kingdom); Murari, A. [Consorzio RFX, Associazione EURATOM-ENEA per la Fusione, Padova (Italy); Tiseanu, I.; Zoita, V. [EURATOM-MEdC Association, Institute for Laser, Plasma and Radiation Physics, Bucharest (Romania)
Highlights: •A new tomographic method for the reconstruction of the 2-D neutron and gamma emissivity on JET. •The method is based on the sparse representation of the reconstructed image in an over-complete dictionary. •Several techniques, based on a priori information are used to regularize this highly limited data set tomographic problem. •The proposed method provides good reconstructions in terms of shapes and resolution. -- Abstract: The JET gamma/neutron profile monitor plasma coverage of the emissive region enables tomographic reconstruction. However, due to the availability of only two projection angles and to the coarse sampling, tomography is a highly limited data set problem. A new reconstruction method, based on the sparse representation of the reconstructed image in an over-complete dictionary, has been developed and applied to JET neutron/gamma tomography. The method has been tested on JET experimental data and significant results are presented. The proposed method provides good reconstructions in terms of shapes and resolution.
Sparse seismic imaging using variable projection
Aravkin, Aleksandr Y.; Tu, Ning; van Leeuwen, Tristan
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using
Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding
Desmal, Abdulla; Bagci, Hakan
A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.
Desmal, Abdulla
Image super-resolution reconstruction based on regularization technique and guided filter
Huang, De-tian; Huang, Wei-qin; Gu, Pei-ting; Liu, Pei-zhong; Luo, Yan-min
In order to improve the accuracy of sparse representation coefficients and the quality of reconstructed images, an improved image super-resolution algorithm based on sparse representation is presented. In the sparse coding stage, the autoregressive (AR) regularization and the non-local (NL) similarity regularization are introduced to improve the sparse coding objective function. A group of AR models which describe the image local structures are pre-learned from the training samples, and one or several suitable AR models can be adaptively selected for each image patch to regularize the solution space. Then, the image non-local redundancy is obtained by the NL similarity regularization to preserve edges. In the process of computing the sparse representation coefficients, the feature-sign search algorithm is utilized instead of the conventional orthogonal matching pursuit algorithm to improve the accuracy of the sparse coefficients. To restore image details further, a global error compensation model based on weighted guided filter is proposed to realize error compensation for the reconstructed images. Experimental results demonstrate that compared with Bicubic, L1SR, SISR, GR, ANR, NE + LS, NE + NNLS, NE + LLE and A + (16 atoms) methods, the proposed approach has remarkable improvement in peak signal-to-noise ratio, structural similarity and subjective visual perception.
An adaptive image sparse reconstruction method combined with nonlocal similarity and cosparsity for mixed Gaussian-Poisson noise removal
Chen, Yong-fei; Gao, Hong-xia; Wu, Zi-ling; Kang, Hui
Compressed sensing (CS) has achieved great success in single noise removal. However, it cannot restore the images contaminated with mixed noise efficiently. This paper introduces nonlocal similarity and cosparsity inspired by compressed sensing to overcome the difficulties in mixed noise removal, in which nonlocal similarity explores the signal sparsity from similar patches, and cosparsity assumes that the signal is sparse after a possibly redundant transform. Meanwhile, an adaptive scheme is designed to keep the balance between mixed noise removal and detail preservation based on local variance. Finally, IRLSM and RACoSaMP are adopted to solve the objective function. Experimental results demonstrate that the proposed method is superior to conventional CS methods, like K-SVD and state-of-art method nonlocally centralized sparse representation (NCSR), in terms of both visual results and quantitative measures.
Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors
He, Xingyu; Tong, Ningning; Hu, Xiaowei
Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.
Effects of sparse sampling schemes on image quality in low-dose CT
Abbas, Sajid; Lee, Taewon; Cho, Seungryong; Shin, Sukyoung; Lee, Rena
Purpose: Various scanning methods and image reconstruction algorithms are actively investigated for low-dose computed tomography (CT) that can potentially reduce a health-risk related to radiation dose. Particularly, compressive-sensing (CS) based algorithms have been successfully developed for reconstructing images from sparsely sampled data. Although these algorithms have shown promises in low-dose CT, it has not been studied how sparse sampling schemes affect image quality in CS-based image reconstruction. In this work, the authors present several sparse-sampling schemes for low-dose CT, quantitatively analyze their data property, and compare effects of the sampling schemes on the image quality.Methods: Data properties of several sampling schemes are analyzed with respect to the CS-based image reconstruction using two measures: sampling density and data incoherence. The authors present five different sparse sampling schemes, and simulated those schemes to achieve a targeted dose reduction. Dose reduction factors of about 75% and 87.5%, compared to a conventional scan, were tested. A fully sampled circular cone-beam CT data set was used as a reference, and sparse sampling has been realized numerically based on the CBCT data.Results: It is found that both sampling density and data incoherence affect the image quality in the CS-based reconstruction. Among the sampling schemes the authors investigated, the sparse-view, many-view undersampling (MVUS)-fine, and MVUS-moving cases have shown promising results. These sampling schemes produced images with similar image quality compared to the reference image and their structure similarity index values were higher than 0.92 in the mouse head scan with 75% dose reduction.Conclusions: The authors found that in CS-based image reconstructions both sampling density and data incoherence affect the image quality, and suggest that a sampling scheme should be devised and optimized by use of these indicators. With this strategic
SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS
A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.
Improved Sparse Channel Estimation for Cooperative Communication Systems
Guan Gui
Full Text Available Accurate channel state information (CSI is necessary at receiver for coherent detection in amplify-and-forward (AF cooperative communication systems. To estimate the channel, traditional methods, that is, least squares (LS and least absolute shrinkage and selection operator (LASSO, are based on assumptions of either dense channel or global sparse channel. However, LS-based linear method neglects the inherent sparse structure information while LASSO-based sparse channel method cannot take full advantage of the prior information. Based on the partial sparse assumption of the cooperative channel model, we propose an improved channel estimation method with partial sparse constraint. At first, by using sparse decomposition theory, channel estimation is formulated as a compressive sensing problem. Secondly, the cooperative channel is reconstructed by LASSO with partial sparse constraint. Finally, numerical simulations are carried out to confirm the superiority of proposed methods over global sparse channel estimation methods.
Sparse Reconstruction for Temperature Distribution Using DTS Fiber Optic Sensors with Applications in Electrical Generator Stator Monitoring
Bazzo, João Paulo; Pipa, Daniel Rodrigues; da Silva, Erlon Vagner; Martelli, Cicero; Cardozo da Silva, Jean Carlos
This paper presents an image reconstruction method to monitor the temperature distribution of electric generator stators. The main objective is to identify insulation failures that may arise as hotspots in the structure. The method is based on temperature readings of fiber optic distributed sensors (DTS) and a sparse reconstruction algorithm. Thermal images of the structure are formed by appropriately combining atoms of a dictionary of hotspots, which was constructed by finite element simulation with a multi-physical model. Due to difficulties for reproducing insulation faults in real stator structure, experimental tests were performed using a prototype similar to the real structure. The results demonstrate the ability of the proposed method to reconstruct images of hotspots with dimensions down to 15 cm, representing a resolution gain of up to six times when compared to the DTS spatial resolution. In addition, satisfactory results were also obtained to detect hotspots with only 5 cm. The application of the proposed algorithm for thermal imaging of generator stators can contribute to the identification of insulation faults in early stages, thereby avoiding catastrophic damage to the structure. PMID:27618040
Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction.
Liu, Yan; Ma, Jianhua; Fan, Yi; Liang, Zhengrong
Previous studies have shown that by minimizing the total variation (TV) of the to-be-estimated image with some data and other constraints, piecewise-smooth x-ray computed tomography (CT) can be reconstructed from sparse-view projection data without introducing notable artifacts. However, due to the piecewise constant assumption for the image, a conventional TV minimization algorithm often suffers from over-smoothness on the edges of the resulting image. To mitigate this drawback, we present an adaptive-weighted TV (AwTV) minimization algorithm in this paper. The presented AwTV model is derived by considering the anisotropic edge property among neighboring image voxels, where the associated weights are expressed as an exponential function and can be adaptively adjusted by the local image-intensity gradient for the purpose of preserving the edge details. Inspired by the previously reported TV-POCS (projection onto convex sets) implementation, a similar AwTV-POCS implementation was developed to minimize the AwTV subject to data and other constraints for the purpose of sparse-view low-dose CT image reconstruction. To evaluate the presented AwTV-POCS algorithm, both qualitative and quantitative studies were performed by computer simulations and phantom experiments. The results show that the presented AwTV-POCS algorithm can yield images with several notable gains, in terms of noise-resolution tradeoff plots and full-width at half-maximum values, as compared to the corresponding conventional TV-POCS algorithm.
Sparse Frequency Waveform Design for Radar-Embedded Communication
Chaoyun Mai
Full Text Available According to the Tag application with function of covert communication, a method for sparse frequency waveform design based on radar-embedded communication is proposed. Firstly, sparse frequency waveforms are designed based on power spectral density fitting and quasi-Newton method. Secondly, the eigenvalue decomposition of the sparse frequency waveform sequence is used to get the dominant space. Finally the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the vertical subspace. Compared with the linear frequency modulation waveform, the sparse frequency waveform can further improve the bandwidth occupation of communication signals, thus achieving higher communication rate. A certain correlation exists between the reciprocally orthogonal communication signals samples and the sparse frequency waveform, which guarantees the low SER (signal error rate and LPI (low probability of intercept. The simulation results verify the effectiveness of this method.
Low-count PET image restoration using sparse representation
Li, Tao; Jiang, Changhui; Gao, Juan; Yang, Yongfeng; Liang, Dong; Liu, Xin; Zheng, Hairong; Hu, Zhanli
In the field of positron emission tomography (PET), reconstructed images are often blurry and contain noise. These problems are primarily caused by the low resolution of projection data. Solving this problem by improving hardware is an expensive solution, and therefore, we attempted to develop a solution based on optimizing several related algorithms in both the reconstruction and image post-processing domains. As sparse technology is widely used, sparse prediction is increasingly applied to solve this problem. In this paper, we propose a new sparse method to process low-resolution PET images. Two dictionaries (D1 for low-resolution PET images and D2 for high-resolution PET images) are learned from a group real PET image data sets. Among these two dictionaries, D1 is used to obtain a sparse representation for each patch of the input PET image. Then, a high-resolution PET image is generated from this sparse representation using D2. Experimental results indicate that the proposed method exhibits a stable and superior ability to enhance image resolution and recover image details. Quantitatively, this method achieves better performance than traditional methods. This proposed strategy is a new and efficient approach for improving the quality of PET images.
Sparse regularization for force identification using dictionaries
Qiao, Baijie; Zhang, Xingwu; Wang, Chenxi; Zhang, Hang; Chen, Xuefeng
The classical function expansion method based on minimizing l2-norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l1-norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases.
A Perceptually Reweighted Mixed-Norm Method for Sparse Approximation of Audio Signals
Christensen, Mads Græsbøll; Sturm, Bob L.
using standard software. A prominent feature of the new method is that it solves a problem that is closely related to the objective of coding, namely rate-distortion optimization. In computer simulations, we demonstrate the properties of the algorithm and its application to real audio signals.......In this paper, we consider the problem of finding sparse representations of audio signals for coding purposes. In doing so, it is of utmost importance that when only a subset of the present components of an audio signal are extracted, it is the perceptually most important ones. To this end, we...... propose a new iterative algorithm based on two principles: 1) a reweighted l1-norm based measure of sparsity; and 2) a reweighted l2-norm based measure of perceptual distortion. Using these measures, the considered problem is posed as a constrained convex optimization problem that can be solved optimally...
An in-depth study of sparse codes on abnormality detection
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no comparative studies of sparse codes regarding abnormality...... are carried out from various angles to better understand the applicability of sparse codes, including computation time, reconstruction error, sparsity, detection accuracy, and their performance combining various detection methods. The experiment results show that combining OMP codes with maximum coordinate...
SparseBeads data: benchmarking sparsity-regularized computed tomography
Jørgensen, Jakob Sauer; Coban, Sophia B.; Lionheart, William R. B.
-regularized reconstruction. A collection of 48 x-ray CT datasets called SparseBeads was designed for benchmarking SR reconstruction algorithms. Beadpacks comprising glass beads of five different sizes as well as mixtures were scanned in a micro-CT scanner to provide structured datasets with variable image sparsity levels...
Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters
Brown, Kristen A.; Harlim, John
In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable
Reconstruction of Micropattern Detector Signals using Convolutional Neural Networks
Flekova, L.; Schott, M.
Micropattern gaseous detector (MPGD) technologies, such as GEMs or MicroMegas, are particularly suitable for precision tracking and triggering in high rate environments. Given their relatively low production costs, MPGDs are an exemplary candidate for the next generation of particle detectors. Having acknowledged these advantages, both the ATLAS and CMS collaborations at the LHC are exploiting these new technologies for their detector upgrade programs in the coming years. When MPGDs are utilized for triggering purposes, the measured signals need to be precisely reconstructed within less than 200 ns, which can be achieved by the usage of FPGAs. In this work, we present a novel approach to identify reconstructed signals, their timing and the corresponding spatial position on the detector. In particular, we study the effect of noise and dead readout strips on the reconstruction performance. Our approach leverages the potential of convolutional neural network (CNNs), which have recently manifested an outstanding performance in a range of modeling tasks. The proposed neural network architecture of our CNN is designed simply enough, so that it can be modeled directly by an FPGA and thus provide precise information on reconstructed signals already in trigger level.
Sparse representation for infrared Dim target detection via a discriminative over-complete dictionary learned online.
Li, Zheng-Zhou; Chen, Jing; Hou, Qian; Fu, Hong-Xia; Dai, Zhen; Jin, Gang; Li, Ru-Zhang; Liu, Chang-Ju
It is difficult for structural over-complete dictionaries such as the Gabor function and discriminative over-complete dictionary, which are learned offline and classified manually, to represent natural images with the goal of ideal sparseness and to enhance the difference between background clutter and target signals. This paper proposes an infrared dim target detection approach based on sparse representation on a discriminative over-complete dictionary. An adaptive morphological over-complete dictionary is trained and constructed online according to the content of infrared image by K-singular value decomposition (K-SVD) algorithm. Then the adaptive morphological over-complete dictionary is divided automatically into a target over-complete dictionary describing target signals, and a background over-complete dictionary embedding background by the criteria that the atoms in the target over-complete dictionary could be decomposed more sparsely based on a Gaussian over-complete dictionary than the one in the background over-complete dictionary. This discriminative over-complete dictionary can not only capture significant features of background clutter and dim targets better than a structural over-complete dictionary, but also strengthens the sparse feature difference between background and target more efficiently than a discriminative over-complete dictionary learned offline and classified manually. The target and background clutter can be sparsely decomposed over their corresponding over-complete dictionaries, yet couldn't be sparsely decomposed based on their opposite over-complete dictionary, so their residuals after reconstruction by the prescribed number of target and background atoms differ very visibly. Some experiments are included and the results show that this proposed approach could not only improve the sparsity more efficiently, but also enhance the performance of small target detection more effectively.
Sparse Representation for Infrared Dim Target Detection via a Discriminative Over-Complete Dictionary Learned Online
Zheng-Zhou Li
Full Text Available It is difficult for structural over-complete dictionaries such as the Gabor function and discriminative over-complete dictionary, which are learned offline and classified manually, to represent natural images with the goal of ideal sparseness and to enhance the difference between background clutter and target signals. This paper proposes an infrared dim target detection approach based on sparse representation on a discriminative over-complete dictionary. An adaptive morphological over-complete dictionary is trained and constructed online according to the content of infrared image by K-singular value decomposition (K-SVD algorithm. Then the adaptive morphological over-complete dictionary is divided automatically into a target over-complete dictionary describing target signals, and a background over-complete dictionary embedding background by the criteria that the atoms in the target over-complete dictionary could be decomposed more sparsely based on a Gaussian over-complete dictionary than the one in the background over-complete dictionary. This discriminative over-complete dictionary can not only capture significant features of background clutter and dim targets better than a structural over-complete dictionary, but also strengthens the sparse feature difference between background and target more efficiently than a discriminative over-complete dictionary learned offline and classified manually. The target and background clutter can be sparsely decomposed over their corresponding over-complete dictionaries, yet couldn't be sparsely decomposed based on their opposite over-complete dictionary, so their residuals after reconstruction by the prescribed number of target and background atoms differ very visibly. Some experiments are included and the results show that this proposed approach could not only improve the sparsity more efficiently, but also enhance the performance of small target detection more effectively.
Sparsely corrupted stimulated scattering signals recovery by iterative reweighted continuous basis pursuit
Wang, Kunpeng; Chai, Yi [College of Automation, Chongqing University, Chongqing 400044 (China); Su, Chunxiao [Research Center of Laser Fusion, CAEP, P. O. Box 919-983, Mianyang 621900 (China)
In this paper, we consider the problem of extracting the desired signals from noisy measurements. This is a classical problem of signal recovery which is of paramount importance in inertial confinement fusion. To accomplish this task, we develop a tractable algorithm based on continuous basis pursuit and reweighted â""{sub 1}-minimization. By modeling the observed signals as superposition of scale time-shifted copies of theoretical waveform, structured noise, and unstructured noise on a finite time interval, a sparse optimization problem is obtained. We propose to solve this problem through an iterative procedure that alternates between convex optimization to estimate the amplitude, and local optimization to estimate the dictionary. The performance of the method was evaluated both numerically and experimentally. Numerically, we recovered theoretical signals embedded in increasing amounts of unstructured noise and compared the results with those obtained through popular denoising methods. We also applied the proposed method to a set of actual experimental data acquired from the Shenguang-II laser whose energy was below the detector noise-equivalent energy. Both simulation and experiments show that the proposed method improves the signal recovery performance and extends the dynamic detection range of detectors.
Wang, Kunpeng; Chai, Yi; Su, Chunxiao
In this paper, we consider the problem of extracting the desired signals from noisy measurements. This is a classical problem of signal recovery which is of paramount importance in inertial confinement fusion. To accomplish this task, we develop a tractable algorithm based on continuous basis pursuit and reweighted â"" 1 -minimization. By modeling the observed signals as superposition of scale time-shifted copies of theoretical waveform, structured noise, and unstructured noise on a finite time interval, a sparse optimization problem is obtained. We propose to solve this problem through an iterative procedure that alternates between convex optimization to estimate the amplitude, and local optimization to estimate the dictionary. The performance of the method was evaluated both numerically and experimentally. Numerically, we recovered theoretical signals embedded in increasing amounts of unstructured noise and compared the results with those obtained through popular denoising methods. We also applied the proposed method to a set of actual experimental data acquired from the Shenguang-II laser whose energy was below the detector noise-equivalent energy. Both simulation and experiments show that the proposed method improves the signal recovery performance and extends the dynamic detection range of detectors
João Paulo Bazzo
Full Text Available This paper presents an image reconstruction method to monitor the temperature distribution of electric generator stators. The main objective is to identify insulation failures that may arise as hotspots in the structure. The method is based on temperature readings of fiber optic distributed sensors (DTS and a sparse reconstruction algorithm. Thermal images of the structure are formed by appropriately combining atoms of a dictionary of hotspots, which was constructed by finite element simulation with a multi-physical model. Due to difficulties for reproducing insulation faults in real stator structure, experimental tests were performed using a prototype similar to the real structure. The results demonstrate the ability of the proposed method to reconstruct images of hotspots with dimensions down to 15 cm, representing a resolution gain of up to six times when compared to the DTS spatial resolution. In addition, satisfactory results were also obtained to detect hotspots with only 5 cm. The application of the proposed algorithm for thermal imaging of generator stators can contribute to the identification of insulation faults in early stages, thereby avoiding catastrophic damage to the structure.
Vector sparse representation of color image using quaternion matrix analysis.
Xu, Yi; Yu, Licheng; Xu, Hongteng; Zhang, Hao; Nguyen, Truong
Traditional sparse image models treat color image pixel as a scalar, which represents color channels separately or concatenate color channels as a monochrome image. In this paper, we propose a vector sparse representation model for color images using quaternion matrix analysis. As a new tool for color image representation, its potential applications in several image-processing tasks are presented, including color image reconstruction, denoising, inpainting, and super-resolution. The proposed model represents the color image as a quaternion matrix, where a quaternion-based dictionary learning algorithm is presented using the K-quaternion singular value decomposition (QSVD) (generalized K-means clustering for QSVD) method. It conducts the sparse basis selection in quaternion space, which uniformly transforms the channel images to an orthogonal color space. In this new color space, it is significant that the inherent color structures can be completely preserved during vector reconstruction. Moreover, the proposed sparse model is more efficient comparing with the current sparse models for image restoration tasks due to lower redundancy between the atoms of different color channels. The experimental results demonstrate that the proposed sparse image model avoids the hue bias issue successfully and shows its potential as a general and powerful tool in color image analysis and processing domain.
Comparison of Methods for Sparse Representation of Musical Signals
Endelt, Line Ørtoft; la Cour-Harbo, Anders
by a number of sparseness measures and results are shown on the â""1 norm of the coefficients, using a dictionary containing a Dirac basis, a Discrete Cosine Transform, and a Wavelet Packet. Evaluated only on the sparseness Matching Pursuit is the best method, and it is also relatively fast....
Joint Group Sparse PCA for Compressed Hyperspectral Imaging.
Khan, Zohaib; Shafait, Faisal; Mian, Ajmal
A sparse principal component analysis (PCA) seeks a sparse linear combination of input features (variables), so that the derived features still explain most of the variations in the data. A group sparse PCA introduces structural constraints on the features in seeking such a linear combination. Collectively, the derived principal components may still require measuring all the input features. We present a joint group sparse PCA (JGSPCA) algorithm, which forces the basic coefficients corresponding to a group of features to be jointly sparse. Joint sparsity ensures that the complete basis involves only a sparse set of input features, whereas the group sparsity ensures that the structural integrity of the features is maximally preserved. We evaluate the JGSPCA algorithm on the problems of compressed hyperspectral imaging and face recognition. Compressed sensing results show that the proposed method consistently outperforms sparse PCA and group sparse PCA in reconstructing the hyperspectral scenes of natural and man-made objects. The efficacy of the proposed compressed sensing method is further demonstrated in band selection for face recognition.
Single and Multiple Object Tracking Using a Multi-Feature Joint Sparse Representation.
Hu, Weiming; Li, Wei; Zhang, Xiaoqin; Maybank, Stephen
In this paper, we propose a tracking algorithm based on a multi-feature joint sparse representation. The templates for the sparse representation can include pixel values, textures, and edges. In the multi-feature joint optimization, noise or occlusion is dealt with using a set of trivial templates. A sparse weight constraint is introduced to dynamically select the relevant templates from the full set of templates. A variance ratio measure is adopted to adaptively adjust the weights of different features. The multi-feature template set is updated adaptively. We further propose an algorithm for tracking multi-objects with occlusion handling based on the multi-feature joint sparse reconstruction. The observation model based on sparse reconstruction automatically focuses on the visible parts of an occluded object by using the information in the trivial templates. The multi-object tracking is simplified into a joint Bayesian inference. The experimental results show the superiority of our algorithm over several state-of-the-art tracking algorithms.
Spectrotemporal CT data acquisition and reconstruction at low dose
Clark, Darin P.; Badea, Cristian T.; Lee, Chang-Lung; Kirsch, David G.
Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction
An Improved Sparse Representation over Learned Dictionary Method for Seizure Detection.
Li, Junhui; Zhou, Weidong; Yuan, Shasha; Zhang, Yanli; Li, Chengcheng; Wu, Qi
Automatic seizure detection has played an important role in the monitoring, diagnosis and treatment of epilepsy. In this paper, a patient specific method is proposed for seizure detection in the long-term intracranial electroencephalogram (EEG) recordings. This seizure detection method is based on sparse representation with online dictionary learning and elastic net constraint. The online learned dictionary could sparsely represent the testing samples more accurately, and the elastic net constraint which combines the 11-norm and 12-norm not only makes the coefficients sparse but also avoids over-fitting problem. First, the EEG signals are preprocessed using wavelet filtering and differential filtering, and the kernel function is applied to make the samples closer to linearly separable. Then the dictionaries of seizure and nonseizure are respectively learned from original ictal and interictal training samples with online dictionary optimization algorithm to compose the training dictionary. After that, the test samples are sparsely coded over the learned dictionary and the residuals associated with ictal and interictal sub-dictionary are calculated, respectively. Eventually, the test samples are classified as two distinct categories, seizure or nonseizure, by comparing the reconstructed residuals. The average segment-based sensitivity of 95.45%, specificity of 99.08%, and event-based sensitivity of 94.44% with false detection rate of 0.23/h and average latency of -5.14 s have been achieved with our proposed method.
Sparse Representations of Hyperspectral Images
Swanson, Robin J.
Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.
SIGNAL RECONSTRUCTION PERFORMANCE OF THE ATLAS HADRONIC TILE CALORIMETER
Do Amaral Coutinho, Y; The ATLAS collaboration
"The Tile Calorimeter for the ATLAS experiment at the CERN Large Hadron Collider (LHC) is a sampling calorimeter with steel as absorber and scintillators as active medium. The scintillators are readout by wavelength shifting fibers coupled to photomultiplier tubes (PMT). The analogue signals from the PMTs are amplified, shaped and digitized by sampling the signal every 25 ns. The TileCal front-end electronics allows to read out the signals produced by about 10000 channels measuring energies ranging from ~30 MeV to ~2 TeV. The read-out system is responsible for reconstructing the data in real-time fulfilling the tight time constraint imposed by the ATLAS first level trigger rate (100 kHz). The main component of the read-out system is the Digital Signal Processor (DSP) which, using an Optimal Filtering reconstruction algorithm, allows to compute for each channel the signal amplitude, time and quality factor at the required high rate. Currently the ATLAS detector and the LHC are undergoing an upgrade program tha...
Analog system for computing sparse codes
Rozell, Christopher John; Johnson, Don Herrick; Baraniuk, Richard Gordon; Olshausen, Bruno A.; Ortman, Robert Lowell
A parallel dynamical system for computing sparse representations of data, i.e., where the data can be fully represented in terms of a small number of non-zero code elements, and for reconstructing compressively sensed images. The system is based on the principles of thresholding and local competition that solves a family of sparse approximation problems corresponding to various sparsity metrics. The system utilizes Locally Competitive Algorithms (LCAs), nodes in a population continually compete with neighboring units using (usually one-way) lateral inhibition to calculate coefficients representing an input in an over complete dictionary.
Greedy vs. L1 convex optimization in sparse coding
Sparse representation has been applied successfully in many image analysis applications, including abnormal event detection, in which a baseline is to learn a dictionary from the training data and detect anomalies from its sparse codes. During this procedure, sparse codes which can be achieved...... solutions. Considering the property of abnormal event detection, i.e., only normal videos are used as training data due to practical reasons, effective codes in classification application may not perform well in abnormality detection. Therefore, we compare the sparse codes and comprehensively evaluate...... their performance from various aspects to better understand their applicability, including computation time, reconstruction error, sparsity, detection...
Signal reconstruction in wireless sensor networks based on a cubature Kalman particle filter
Huang Jin-Wang; Feng Jiu-Chao
For solving the issues of the signal reconstruction of nonlinear non-Gaussian signals in wireless sensor networks (WSNs), a new signal reconstruction algorithm based on a cubature Kalman particle filter (CKPF) is proposed in this paper. We model the reconstruction signal first and then use the CKPF to estimate the signal. The CKPF uses a cubature Kalman filter (CKF) to generate the importance proposal distribution of the particle filter and integrates the latest observation, which can approximate the true posterior distribution better. It can improve the estimation accuracy. CKPF uses fewer cubature points than the unscented Kalman particle filter (UKPF) and has less computational overheads. Meanwhile, CKPF uses the square root of the error covariance for iterating and is more stable and accurate than the UKPF counterpart. Simulation results show that the algorithm can reconstruct the observed signals quickly and effectively, at the same time consuming less computational time and with more accuracy than the method based on UKPF. (general)
Blind Compressed Sensing Parameter Estimation of Non-cooperative Frequency Hopping Signal
Chen Ying
Full Text Available To overcome the disadvantages of a non-cooperative frequency hopping communication system, such as a high sampling rate and inadequate prior information, parameter estimation based on Blind Compressed Sensing (BCS is proposed. The signal is precisely reconstructed by the alternating iteration of sparse coding and basis updating, and the hopping frequencies are directly estimated based on the results. Compared with conventional compressive sensing, blind compressed sensing does not require prior information of the frequency hopping signals; hence, it offers an effective solution to the inadequate prior information problem. In the proposed method, the signal is first modeled and then reconstructed by Orthonormal Block Diagonal Blind Compressed Sensing (OBD-BCS, and the hopping frequencies and hop period are finally estimated. The simulation results suggest that the proposed method can reconstruct and estimate the parameters of noncooperative frequency hopping signals with a low signal-to-noise ratio.
Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint
Zhi Gao
Full Text Available Light detection and ranging (LiDAR sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs and unmanned aerial vehicles (UAVs to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency.
Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint.
Gao, Zhi; Lao, Mingjie; Sang, Yongsheng; Wen, Fei; Ramesh, Bharath; Zhai, Ruifang
Light detection and ranging (LiDAR) sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency.
Incomplete projection reconstruction of computed tomography based on the modified discrete algebraic reconstruction technique
Yang, Fuqiang; Zhang, Dinghua; Huang, Kuidong; Gao, Zongzhao; Yang, YaFei
Based on the discrete algebraic reconstruction technique (DART), this study aims to address and test a new improved algorithm applied to incomplete projection data to generate a high quality reconstruction image by reducing the artifacts and noise in computed tomography. For the incomplete projections, an augmented Lagrangian based on compressed sensing is first used in the initial reconstruction for segmentation of the DART to get higher contrast graphics for boundary and non-boundary pixels. Then, the block matching 3D filtering operator was used to suppress the noise and to improve the gray distribution of the reconstructed image. Finally, simulation studies on the polychromatic spectrum were performed to test the performance of the new algorithm. Study results show a significant improvement in the signal-to-noise ratios (SNRs) and average gradients (AGs) of the images reconstructed from incomplete data. The SNRs and AGs of the new images reconstructed by DART-ALBM were on average 30%-40% and 10% higher than the images reconstructed by DART algorithms. Since the improved DART-ALBM algorithm has a better robustness to limited-view reconstruction, which not only makes the edge of the image clear but also makes the gray distribution of non-boundary pixels better, it has the potential to improve image quality from incomplete projections or sparse projections.
Compressed Sensing, Pseudodictionary-Based, Superresolution Reconstruction
Chun-mei Li
Full Text Available The spatial resolution of digital images is the critical factor that affects photogrammetry precision. Single-frame, superresolution, image reconstruction is a typical underdetermined, inverse problem. To solve this type of problem, a compressive, sensing, pseudodictionary-based, superresolution reconstruction method is proposed in this study. The proposed method achieves pseudodictionary learning with an available low-resolution image and uses the K-SVD algorithm, which is based on the sparse characteristics of the digital image. Then, the sparse representation coefficient of the low-resolution image is obtained by solving the norm of l0 minimization problem, and the sparse coefficient and high-resolution pseudodictionary are used to reconstruct image tiles with high resolution. Finally, single-frame-image superresolution reconstruction is achieved. The proposed method is applied to photogrammetric images, and the experimental results indicate that the proposed method effectively increase image resolution, increase image information content, and achieve superresolution reconstruction. The reconstructed results are better than those obtained from traditional interpolation methods in aspect of visual effects and quantitative indicators.
Multilevel sparse functional principal component analysis.
Di, Chongzhi; Crainiceanu, Ciprian M; Jank, Wolfgang S
We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we consider the case when functions are sparsely sampled and may contain only a few observations per function. We exploit the multilevel structure of covariance operators and achieve data reduction by principal component decompositions at both between and within subject levels. We address inherent methodological differences in the sparse sampling context to: 1) estimate the covariance operators; 2) estimate the functional principal component scores; 3) predict the underlying curves. Through simulations the proposed method is able to discover dominating modes of variations and reconstruct underlying curves well even in sparse settings. Our approach is illustrated by two applications, the Sleep Heart Health Study and eBay auctions.
Signal process and profile reconstruction of stress corrosion crack by eddy current test
Zhang Siquan; Chen Tiequn; Liu Guixiong
The reconstruction of crack profiles is very important in the NDE (nondestructive evaluation) of critical structures, such as pressure vessel and tubes in heat exchangers. First a wavelet transform signal processing technique is used to reduce noise and other non-defect signals from the signals of crack, and then based on an artificial neural network method, the crack profiles are reconstructed. Although the results reveal that this method is with many advantages such as a short CPU time and precision for reconstruction,it does have some drawbacks, for example, the database generation and network training is a much time consuming work. Moreover, this approach does not expressly reconstruct the distribution of conductivity inside a crack, so the reliability of a reconstructed crack shape is unknown. But in practical application, if we do not consider the multiple cracks, this method can be used to reconstruct the natural crack. (authors)
Robust Fringe Projection Profilometry via Sparse Representation.
Budianto; Lun, Daniel P K
In this paper, a robust fringe projection profilometry (FPP) algorithm using the sparse dictionary learning and sparse coding techniques is proposed. When reconstructing the 3D model of objects, traditional FPP systems often fail to perform if the captured fringe images have a complex scene, such as having multiple and occluded objects. It introduces great difficulty to the phase unwrapping process of an FPP system that can result in serious distortion in the final reconstructed 3D model. For the proposed algorithm, it encodes the period order information, which is essential to phase unwrapping, into some texture patterns and embeds them to the projected fringe patterns. When the encoded fringe image is captured, a modified morphological component analysis and a sparse classification procedure are performed to decode and identify the embedded period order information. It is then used to assist the phase unwrapping process to deal with the different artifacts in the fringe images. Experimental results show that the proposed algorithm can significantly improve the robustness of an FPP system. It performs equally well no matter the fringe images have a simple or complex scene, or are affected due to the ambient lighting of the working environment.
Framing U-Net via Deep Convolutional Framelets: Application to Sparse-View CT.
Han, Yoseob; Ye, Jong Chul
X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse-view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and tight frame U-Nets satisfy the so-called frame condition which makes them better for effective recovery of high frequency edges in sparse-view CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.
Narrowband Interference Mitigation in SC-FDMA Using Bayesian Sparse Recovery
This paper presents a novel narrowband interference (NBI) mitigation scheme for single carrier-frequency division multiple access systems. The proposed NBI cancellation scheme exploits the frequency-domain sparsity of the unknown signal and adopts a low complexity Bayesian sparse recovery procedure. At the transmitter, a few randomly chosen data locations are kept data free to sense the NBI signal at the receiver. Furthermore, it is noted that in practice, the sparsity of the NBI signal is destroyed by a grid mismatch between the NBI sources and the system under consideration. Toward this end, first, an accurate grid mismatch model is presented that is capable of assuming independent offsets for multiple NBI sources, and second, the sparsity of the unknown signal is restored prior to reconstruction using a sparsifying transform. To improve the spectral efficiency of the proposed scheme, a data-aided NBI recovery procedure is outlined that relies on adaptively selecting a subset of data-points and using them as additional measurements. Numerical results demonstrate the effectiveness of the proposed scheme for NBI mitigation.
Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
Ensslin, Torsten A.; Frommert, Mona
The optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters. If these are not known a priori, they have to be measured simultaneously from the same data used for the signal reconstruction. We formulate the general problem of signal inference in the presence of unknown parameters within the framework of information field theory. To solve this, we develop a generic parameter-uncertainty renormalized estimation (PURE) technique. As a concrete application, we address the problem of reconstructing Gaussian signals with unknown power-spectrum with five different approaches: (i) separate maximum-a-posteriori power-spectrum measurement and subsequent reconstruction, (ii) maximum-a-posteriori reconstruction with marginalized power-spectrum, (iii) maximizing the joint posterior of signal and spectrum, (iv) guessing the spectrum from the variance in the Wiener-filter map, and (v) renormalization flow analysis of the field-theoretical problem providing the PURE filter. In all cases, the reconstruction can be described or approximated as Wiener-filter operations with assumed signal spectra derived from the data according to the same recipe, but with differing coefficients. All of these filters, except the renormalized one, exhibit a perception threshold in case of a Jeffreys prior for the unknown spectrum. Data modes with variance below this threshold do not affect the signal reconstruction at all. Filter (iv) seems to be similar to the so-called Karhune-Loeve and Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology, which therefore should also exhibit a marginal perception threshold if correctly implemented. We present statistical performance tests and show that the PURE filter is superior to the others, especially if the post-Wiener-filter corrections are included or in case an additional scale-independent spectral smoothness prior can be adopted.
Microstructure Images Restoration of Metallic Materials Based upon KSVD and Smoothing Penalty Sparse Representation Approach.
Li, Qing; Liang, Steven Y
Microstructure images of metallic materials play a significant role in industrial applications. To address image degradation problem of metallic materials, a novel image restoration technique based on K-means singular value decomposition (KSVD) and smoothing penalty sparse representation (SPSR) algorithm is proposed in this work, the microstructure images of aluminum alloy 7075 (AA7075) material are used as examples. To begin with, to reflect the detail structure characteristics of the damaged image, the KSVD dictionary is introduced to substitute the traditional sparse transform basis (TSTB) for sparse representation. Then, due to the image restoration, modeling belongs to a highly underdetermined equation, and traditional sparse reconstruction methods may cause instability and obvious artifacts in the reconstructed images, especially reconstructed image with many smooth regions and the noise level is strong, thus the SPSR (here, q = 0.5) algorithm is designed to reconstruct the damaged image. The results of simulation and two practical cases demonstrate that the proposed method has superior performance compared with some state-of-the-art methods in terms of restoration performance factors and visual quality. Meanwhile, the grain size parameters and grain boundaries of microstructure image are discussed before and after they are restored by proposed method.
Method and apparatus for reconstructing in-cylinder pressure and correcting for signal decay
Huang, Jian
A method comprises steps for reconstructing in-cylinder pressure data from a vibration signal collected from a vibration sensor mounted on an engine component where it can generate a signal with a high signal-to-noise ratio, and correcting the vibration signal for errors introduced by vibration signal charge decay and sensor sensitivity. The correction factors are determined as a function of estimated motoring pressure and the measured vibration signal itself with each of these being associated with the same engine cycle. Accordingly, the method corrects for charge decay and changes in sensor sensitivity responsive to different engine conditions to allow greater accuracy in the reconstructed in-cylinder pressure data. An apparatus is also disclosed for practicing the disclosed method, comprising a vibration sensor, a data acquisition unit for receiving the vibration signal, a computer processing unit for processing the acquired signal and a controller for controlling the engine operation based on the reconstructed in-cylinder pressure.
Reconstruction of systems with impulses and delays from time series data
Jeon, Jong-ha; Kim, Pilwon
In this paper, we present an approach to identification of dynamical systems with irregular impulses and time delays. The suggested method enables one to reconstruct the underlying differential equations, using the l 1 -minimization technique in signal processing which takes advantage of the signal's sparseness. Based on the idea that irregular impulses can be regarded as sparse error in the fitting procedure, we obtain an efficient algorithm for reconstructions that separates the regular parts of dynamics from impulsive ones. From time series data sampled from an impulsive ecological models, the suggested method restores an essential dynamics of the original systems. The method also applies to chaotic systems perturbed by intermittent impacts and successfully captures dynamics reflecting qualitative behavior independent of impacts. In addition, we can identify a time-delay Lotka–Volterra model with no prior information on delay time given, to which conventional parameter estimate methods are hardly applicable
Semi-blind sparse image reconstruction with application to MRFM.
Park, Se Un; Dobigeon, Nicolas; Hero, Alfred O
We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high-dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.
Reconstructing events, from electronic signals to tracks
CERN. Geneva
Reconstructing tracks in the events taken by LHC experiments is one of the most challenging and computationally expensive software tasks to be carried out in the data processing chain. A typical LHC event is composed of multiple p-p interactions, each leaving signals from many charged particles in the detector and jus building up an environment of unprecedented complexity. In the lecture I will give an overview of event reconstruction in a typical High Energy Physics experiment. After an introduction to particle tracking detectors I will discuss the concepts and techniques required to master the tracking challenge at the LHC. I will explain how track propagation in a realistic detector works, present different techniques for track fitting and track finding. At the end we will see how all of those techniques play together in the ATLAS track reconstruction application.
Sparse Bayesian Learning for DOA Estimation with Mutual Coupling
Jisheng Dai
Full Text Available Sparse Bayesian learning (SBL has given renewed interest to the problem of direction-of-arrival (DOA estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs. Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.
Sparse-View Ultrasound Diffraction Tomography Using Compressed Sensing with Nonuniform FFT
Shaoyan Hua
Full Text Available Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT. In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed.
Light field reconstruction robust to signal dependent noise
Ren, Kun; Bian, Liheng; Suo, Jinli; Dai, Qionghai
Capturing four dimensional light field data sequentially using a coded aperture camera is an effective approach but suffers from low signal noise ratio. Although multiplexing can help raise the acquisition quality, noise is still a big issue especially for fast acquisition. To address this problem, this paper proposes a noise robust light field reconstruction method. Firstly, scene dependent noise model is studied and incorporated into the light field reconstruction framework. Then, we derive an optimization algorithm for the final reconstruction. We build a prototype by hacking an off-the-shelf camera for data capturing and prove the concept. The effectiveness of this method is validated with experiments on the real captured data.
Reconstruction of sound source signal by analytical passive TR in the environment with airflow
Wei, Long; Li, Min; Yang, Debin; Niu, Feng; Zeng, Wu
In the acoustic design of air vehicles, the time-domain signals of noise sources on the surface of air vehicles can serve as data support to reveal the noise source generation mechanism, analyze acoustic fatigue, and take measures for noise insulation and reduction. To rapidly reconstruct the time-domain sound source signals in an environment with flow, a method combining the analytical passive time reversal mirror (AP-TR) with a shear flow correction is proposed. In this method, the negative influence of flow on sound wave propagation is suppressed by the shear flow correction, obtaining the corrected acoustic propagation time delay and path. Those corrected time delay and path together with the microphone array signals are then submitted to the AP-TR, reconstructing more accurate sound source signals in the environment with airflow. As an analytical method, AP-TR offers a supplementary way in 3D space to reconstruct the signal of sound source in the environment with airflow instead of the numerical TR. Experiments on the reconstruction of the sound source signals of a pair of loud speakers are conducted in an anechoic wind tunnel with subsonic airflow to validate the effectiveness and priorities of the proposed method. Moreover the comparison by theorem and experiment result between the AP-TR and the time-domain beamforming in reconstructing the sound source signal is also discussed.
Robust representation and recognition of facial emotions using extreme sparse learning.
Shojaeilangari, Seyedehsamaneh; Yau, Wei-Yun; Nandakumar, Karthik; Li, Jun; Teoh, Eam Khwang
Recognition of natural emotions from human faces is an interesting topic with a wide range of potential applications, such as human-computer interaction, automated tutoring systems, image and video retrieval, smart environments, and driver warning systems. Traditionally, facial emotion recognition systems have been evaluated on laboratory controlled data, which is not representative of the environment faced in real-world applications. To robustly recognize the facial emotions in real-world natural situations, this paper proposes an approach called extreme sparse learning, which has the ability to jointly learn a dictionary (set of basis) and a nonlinear classification model. The proposed approach combines the discriminative power of extreme learning machine with the reconstruction property of sparse representation to enable accurate classification when presented with noisy signals and imperfect data recorded in natural settings. In addition, this paper presents a new local spatio-temporal descriptor that is distinctive and pose-invariant. The proposed framework is able to achieve the state-of-the-art recognition accuracy on both acted and spontaneous facial emotion databases.
Learning Joint-Sparse Codes for Calibration-Free Parallel MR Imaging.
Wang, Shanshan; Tan, Sha; Gao, Yuan; Liu, Qiegen; Ying, Leslie; Xiao, Taohui; Liu, Yuanyuan; Liu, Xin; Zheng, Hairong; Liang, Dong
The integration of compressed sensing and parallel imaging (CS-PI) has shown an increased popularity in recent years to accelerate magnetic resonance (MR) imaging. Among them, calibration-free techniques have presented encouraging performances due to its capability in robustly handling the sensitivity information. Unfortunately, existing calibration-free methods have only explored joint-sparsity with direct analysis transform projections. To further exploit joint-sparsity and improve reconstruction accuracy, this paper proposes to Learn joINt-sparse coDes for caliBration-free parallEl mR imaGing (LINDBERG) by modeling the parallel MR imaging problem as an - - minimization objective with an norm constraining data fidelity, Frobenius norm enforcing sparse representation error and the mixed norm triggering joint sparsity across multichannels. A corresponding algorithm has been developed to alternatively update the sparse representation, sensitivity encoded images and K-space data. Then, the final image is produced as the square root of sum of squares of all channel images. Experimental results on both physical phantom and in vivo data sets show that the proposed method is comparable and even superior to state-of-the-art CS-PI reconstruction approaches. Specifically, LINDBERG has presented strong capability in suppressing noise and artifacts while reconstructing MR images from highly undersampled multichannel measurements.
Obtaining sparse distributions in 2D inverse problems
Reci, A; Sederman, Andrew John; Gladden, Lynn Faith
The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxat...
Single image super-resolution based on compressive sensing and improved TV minimization sparse recovery
Vishnukumar, S.; Wilscy, M.
In this paper, we propose a single image Super-Resolution (SR) method based on Compressive Sensing (CS) and Improved Total Variation (TV) Minimization Sparse Recovery. In the CS framework, low-resolution (LR) image is treated as the compressed version of high-resolution (HR) image. Dictionary Training and Sparse Recovery are the two phases of the method. K-Singular Value Decomposition (K-SVD) method is used for dictionary training and the dictionary represents HR image patches in a sparse manner. Here, only the interpolated version of the LR image is used for training purpose and thereby the structural self similarity inherent in the LR image is exploited. In the sparse recovery phase the sparse representation coefficients with respect to the trained dictionary for LR image patches are derived using Improved TV Minimization method. HR image can be reconstructed by the linear combination of the dictionary and the sparse coefficients. The experimental results show that the proposed method gives better results quantitatively as well as qualitatively on both natural and remote sensing images. The reconstructed images have better visual quality since edges and other sharp details are preserved.
Distributed fiber sparse-wideband vibration sensing by sub-Nyquist additive random sampling
Zhang, Jingdong; Zheng, Hua; Zhu, Tao; Yin, Guolu; Liu, Min; Bai, Yongzhong; Qu, Dingrong; Qiu, Feng; Huang, Xianbing
The round trip time of the light pulse limits the maximum detectable vibration frequency response range of phase-sensitive optical time domain reflectometry ({\\phi}-OTDR). Unlike the uniform laser pulse interval in conventional {\\phi}-OTDR, we randomly modulate the pulse interval, so that an equivalent sub-Nyquist additive random sampling (sNARS) is realized for every sensing point of the long interrogation fiber. For an {\\phi}-OTDR system with 10 km sensing length, the sNARS method is optimized by theoretical analysis and Monte Carlo simulation, and the experimental results verify that a wide-band spars signal can be identified and reconstructed. Such a method can broaden the vibration frequency response range of {\\phi}-OTDR, which is of great significance in sparse-wideband-frequency vibration signal detection, such as rail track monitoring and metal defect detection.
Exhaustive Search for Sparse Variable Selection in Linear Regression
Igarashi, Yasuhiko; Takenaka, Hikaru; Nakanishi-Ohno, Yoshinori; Uemura, Makoto; Ikeda, Shiro; Okada, Masato
We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.
Reconstruction of gastric slow wave from finger photoplethysmographic signal using radial basis function neural network.
Mohamed Yacin, S; Srinivasa Chakravarthy, V; Manivannan, M
Extraction of extra-cardiac information from photoplethysmography (PPG) signal is a challenging research problem with significant clinical applications. In this study, radial basis function neural network (RBFNN) is used to reconstruct the gastric myoelectric activity (GMA) slow wave from finger PPG signal. Finger PPG and GMA (measured using Electrogastrogram, EGG) signals were acquired simultaneously at the sampling rate of 100 Hz from ten healthy subjects. Discrete wavelet transform (DWT) was used to extract slow wave (0-0.1953 Hz) component from the finger PPG signal; this slow wave PPG was used to reconstruct EGG. A RBFNN is trained on signals obtained from six subjects in both fasting and postprandial conditions. The trained network is tested on data obtained from the remaining four subjects. In the earlier study, we have shown the presence of GMA information in finger PPG signal using DWT and cross-correlation method. In this study, we explicitly reconstruct gastric slow wave from finger PPG signal by the proposed RBFNN-based method. It was found that the network-reconstructed slow wave provided significantly higher (P wave than the correlation obtained (≈0.7) between the PPG slow wave from DWT and the EEG slow wave. Our results showed that a simple finger PPG signal can be used to reconstruct gastric slow wave using RBFNN method.
Joint reconstruction of dynamic PET activity and kinetic parametric images using total variation constrained dictionary sparse coding
Yu, Haiqing; Chen, Shuhang; Chen, Yunmei; Liu, Huafeng
Dynamic positron emission tomography (PET) is capable of providing both spatial and temporal information of radio tracers in vivo. In this paper, we present a novel joint estimation framework to reconstruct temporal sequences of dynamic PET images and the coefficients characterizing the system impulse response function, from which the associated parametric images of the system macro parameters for tracer kinetics can be estimated. The proposed algorithm, which combines statistical data measurement and tracer kinetic models, integrates a dictionary sparse coding (DSC) into a total variational minimization based algorithm for simultaneous reconstruction of the activity distribution and parametric map from measured emission sinograms. DSC, based on the compartmental theory, provides biologically meaningful regularization, and total variation regularization is incorporated to provide edge-preserving guidance. We rely on techniques from minimization algorithms (the alternating direction method of multipliers) to first generate the estimated activity distributions with sub-optimal kinetic parameter estimates, and then recover the parametric maps given these activity estimates. These coupled iterative steps are repeated as necessary until convergence. Experiments with synthetic, Monte Carlo generated data, and real patient data have been conducted, and the results are very promising.
Skull Defects in Finite Element Head Models for Source Reconstruction from Magnetoencephalography Signals
Lau, Stephan; Güllmar, Daniel; Flemming, Lars; Grayden, David B.; Cook, Mark J.; Wolters, Carsten H.; Haueisen, Jens
Magnetoencephalography (MEG) signals are influenced by skull defects. However, there is a lack of evidence of this influence during source reconstruction. Our objectives are to characterize errors in source reconstruction from MEG signals due to ignoring skull defects and to assess the ability of an exact finite element head model to eliminate such errors. A detailed finite element model of the head of a rabbit used in a physical experiment was constructed from magnetic resonance and co-registered computer tomography imaging that differentiated nine tissue types. Sources of the MEG measurements above intact skull and above skull defects respectively were reconstructed using a finite element model with the intact skull and one incorporating the skull defects. The forward simulation of the MEG signals reproduced the experimentally observed characteristic magnitude and topography changes due to skull defects. Sources reconstructed from measured MEG signals above intact skull matched the known physical locations and orientations. Ignoring skull defects in the head model during reconstruction displaced sources under a skull defect away from that defect. Sources next to a defect were reoriented. When skull defects, with their physical conductivity, were incorporated in the head model, the location and orientation errors were mostly eliminated. The conductivity of the skull defect material non-uniformly modulated the influence on MEG signals. We propose concrete guidelines for taking into account conducting skull defects during MEG coil placement and modeling. Exact finite element head models can improve localization of brain function, specifically after surgery. PMID:27092044
Optimal Couple Projections for Domain Adaptive Sparse Representation-based Classification.
Zhang, Guoqing; Sun, Huaijiang; Porikli, Fatih; Liu, Yazhou; Sun, Quansen
In recent years, sparse representation based classification (SRC) is one of the most successful methods and has been shown impressive performance in various classification tasks. However, when the training data has a different distribution than the testing data, the learned sparse representation may not be optimal, and the performance of SRC will be degraded significantly. To address this problem, in this paper, we propose an optimal couple projections for domain-adaptive sparse representation-based classification (OCPD-SRC) method, in which the discriminative features of data in the two domains are simultaneously learned with the dictionary that can succinctly represent the training and testing data in the projected space. OCPD-SRC is designed based on the decision rule of SRC, with the objective to learn coupled projection matrices and a common discriminative dictionary such that the between-class sparse reconstruction residuals of data from both domains are maximized, and the within-class sparse reconstruction residuals of data are minimized in the projected low-dimensional space. Thus, the resulting representations can well fit SRC and simultaneously have a better discriminant ability. In addition, our method can be easily extended to multiple domains and can be kernelized to deal with the nonlinear structure of data. The optimal solution for the proposed method can be efficiently obtained following the alternative optimization method. Extensive experimental results on a series of benchmark databases show that our method is better or comparable to many state-of-the-art methods.
Adaptive wavelet tight frame construction for accelerating MRI reconstruction
Genjiao Zhou
Full Text Available The sparsity regularization approach, which assumes that the image of interest is likely to have sparse representation in some transform domain, has been an active research area in image processing and medical image reconstruction. Although various sparsifying transforms have been used in medical image reconstruction such as wavelet, contourlet, and total variation (TV etc., the efficiency of these transforms typically rely on the special structure of the underlying image. A better way to address this issue is to develop an overcomplete dictionary from the input data in order to get a better sparsifying transform for the underlying image. However, the general overcomplete dictionaries do not satisfy the so-called perfect reconstruction property which ensures that the given signal can be perfectly represented by its canonical coefficients in a manner similar to orthonormal bases, resulting in time consuming in the iterative image reconstruction. This work is to develop an adaptive wavelet tight frame method for magnetic resonance image reconstruction. The proposed scheme incorporates the adaptive wavelet tight frame approach into the magnetic resonance image reconstruction by solving a l0-regularized minimization problem. Numerical results show that the proposed approach provides significant time savings as compared to the over-complete dictionary based methods with comparable performance in terms of both peak signal-to-noise ratio and subjective visual quality.
Reconstruction of magnetic resonance imaging by three-dimensional dual-dictionary learning.
Song, Ying; Zhu, Zhen; Lu, Yang; Liu, Qiegen; Zhao, Jun
To improve the magnetic resonance imaging (MRI) data acquisition speed while maintaining the reconstruction quality, a novel method is proposed for multislice MRI reconstruction from undersampled k-space data based on compressed-sensing theory using dictionary learning. There are two aspects to improve the reconstruction quality. One is that spatial correlation among slices is used by extending the atoms in dictionary learning from patches to blocks. The other is that the dictionary-learning scheme is used at two resolution levels; i.e., a low-resolution dictionary is used for sparse coding and a high-resolution dictionary is used for image updating. Numerical experiments are carried out on in vivo 3D MR images of brains and abdomens with a variety of undersampling schemes and ratios. The proposed method (dual-DLMRI) achieves better reconstruction quality than conventional reconstruction methods, with the peak signal-to-noise ratio being 7 dB higher. The advantages of the dual dictionaries are obvious compared with the single dictionary. Parameter variations ranging from 50% to 200% only bias the image quality within 15% in terms of the peak signal-to-noise ratio. Dual-DLMRI effectively uses the a priori information in the dual-dictionary scheme and provides dramatically improved reconstruction quality. Copyright © 2013 Wiley Periodicals, Inc.
Local posterior concentration rate for multilevel sparse sequences
Belitser, E.N.; Nurushev, N.
We consider empirical Bayesian inference in the many normal means model in the situation when the high-dimensional mean vector is multilevel sparse, that is,most of the entries of the parameter vector are some fixed values. For instance, the traditional sparse signal is a particular case (with one
Variational 3D-PIV with sparse descriptors
Lasinger, Katrin; Vogel, Christoph; Pock, Thomas; Schindler, Konrad
3D particle imaging velocimetry (3D-PIV) aims to recover the flow field in a volume of fluid, which has been seeded with tracer particles and observed from multiple camera viewpoints. The first step of 3D-PIV is to reconstruct the 3D locations of the tracer particles from synchronous views of the volume. We propose a new method for iterative particle reconstruction, in which the locations and intensities of all particles are inferred in one joint energy minimization. The energy function is designed to penalize deviations between the reconstructed 3D particles and the image evidence, while at the same time aiming for a sparse set of particles. We find that the new method, without any post-processing, achieves significantly cleaner particle volumes than a conventional, tomographic MART reconstruction, and can handle a wide range of particle densities. The second step of 3D-PIV is to then recover the dense motion field from two consecutive particle reconstructions. We propose a variational model, which makes it possible to directly include physical properties, such as incompressibility and viscosity, in the estimation of the motion field. To further exploit the sparse nature of the input data, we propose a novel, compact descriptor of the local particle layout. Hence, we avoid the memory-intensive storage of high-resolution intensity volumes. Our framework is generic and allows for a variety of different data costs (correlation measures) and regularizers. We quantitatively evaluate it with both the sum of squared differences and the normalized cross-correlation, respectively with both a hard and a soft version of the incompressibility constraint.
WSNs Microseismic Signal Subsection Compression Algorithm Based on Compressed Sensing
Zhouzhou Liu
Full Text Available For wireless network microseismic monitoring and the problems of low compression ratio and high energy consumption of communication, this paper proposes a segmentation compression algorithm according to the characteristics of the microseismic signals and the compression perception theory (CS used in the transmission process. The algorithm will be collected as a number of nonzero elements of data segmented basis, by reducing the number of combinations of nonzero elements within the segment to improve the accuracy of signal reconstruction, while taking advantage of the characteristics of compressive sensing theory to achieve a high compression ratio of the signal. Experimental results show that, in the quantum chaos immune clone refactoring (Q-CSDR algorithm for reconstruction algorithm, under the condition of signal sparse degree higher than 40, to be more than 0.4 of the compression ratio to compress the signal, the mean square error is less than 0.01, prolonging the network life by 2 times.
Image understanding using sparse representations
Thiagarajan, Jayaraman J; Turaga, Pavan; Spanias, Andreas
Image understanding has been playing an increasingly crucial role in several inverse problems and computer vision. Sparse models form an important component in image understanding, since they emulate the activity of neural receptors in the primary visual cortex of the human brain. Sparse methods have been utilized in several learning problems because of their ability to provide parsimonious, interpretable, and efficient models. Exploiting the sparsity of natural signals has led to advances in several application areas including image compression, denoising, inpainting, compressed sensing, blin
Robust reconstruction of a signal from its unthresholded recurrence plot subject to disturbances
Sipers, Aloys, E-mail: aloys.sipers@zuyd.nl [Department of Bèta Sciences and Technology, Zuyd University (Netherlands); Borm, Paul, E-mail: paul.borm@zuyd.nl [Department of Bèta Sciences and Technology, Zuyd University (Netherlands); Peeters, Ralf, E-mail: ralf.peeters@maastrichtuniversity.nl [Department of Data Science and Knowledge Engineering, Maastricht University (Netherlands)
To make valid inferences from recurrence plots for time-delay embedded signals, two underlying key questions are: (1) to what extent does an unthresholded recurrence (URP) plot carry the same information as the signal that generated it, and (2) how does the information change when the URP gets distorted. We studied the first question in our earlier work , where it was shown that the URP admits the reconstruction of the underlying signal (up to its mean and a choice of sign) if and only if an associated graph is connected. Here we refine this result and we give an explicit condition in terms of the embedding parameters and the discrete Fourier spectrum of the URP. We also develop a method for the reconstruction of the underlying signal which overcomes several drawbacks that earlier approaches had. To address the second question we investigate robustness of the proposed reconstruction method under disturbances. We carry out two simulation experiments which are characterized by a broad band and a narrow band spectrum respectively. For each experiment we choose a noise level and two different pairs of embedding parameters. The conventional binary recurrence plot (RP) is obtained from the URP by thresholding and zero-one conversion, which can be viewed as severe distortion acting on the URP. Typically the reconstruction of the underlying signal from an RP is expected to be rather inaccurate. However, by introducing the concept of a multi-level recurrence plot (MRP) we propose to bridge the information gap between the URP and the RP, while still achieving a high data compression rate. We demonstrate the working of the proposed reconstruction procedure on MRPs, indicating that MRPs with just a few discretization levels can usually capture signal properties and morphologies more accurately than conventional RPs. - Highlights: • A recurrence plot is maximally informative if and only if the corresponding graph is connected. • The diameter of the connected graph is always
Intelligent condition monitoring method for bearing faults from highly compressed measurements using sparse over-complete features
Ahmed, H. O. A.; Wong, M. L. D.; Nandi, A. K.
Condition classification of rolling element bearings in rotating machines is important to prevent the breakdown of industrial machinery. A considerable amount of literature has been published on bearing faults classification. These studies aim to determine automatically the current status of a roller element bearing. Of these studies, methods based on compressed sensing (CS) have received some attention recently due to their ability to allow one to sample below the Nyquist sampling rate. This technology has many possible uses in machine condition monitoring and has been investigated as a possible approach for fault detection and classification in the compressed domain, i.e., without reconstructing the original signal. However, previous CS based methods have been found to be too weak for highly compressed data. The present paper explores computationally, for the first time, the effects of sparse autoencoder based over-complete sparse representations on the classification performance of highly compressed measurements of bearing vibration signals. For this study, the CS method was used to produce highly compressed measurements of the original bearing dataset. Then, an effective deep neural network (DNN) with unsupervised feature learning algorithm based on sparse autoencoder is used for learning over-complete sparse representations of these compressed datasets. Finally, the fault classification is achieved using two stages, namely, pre-training classification based on stacked autoencoder and softmax regression layer form the deep net stage (the first stage), and re-training classification based on backpropagation (BP) algorithm forms the fine-tuning stage (the second stage). The experimental results show that the proposed method is able to achieve high levels of accuracy even with extremely compressed measurements compared with the existing techniques.
Evaluation of image collection requirements for 3D reconstruction using phototourism techniques on sparse overhead data
Ontiveros, Erin; Salvaggio, Carl; Nilosek, David; Raqueño, Nina; Faulring, Jason
Phototourism is a burgeoning field that uses collections of ground-based photographs to construct a three-dimensional model of a tourist site, using computer vision techniques. These techniques capitalize on the extensive overlap generated by the various visitor-acquired images from which a three-dimensional point cloud can be generated. From there, a facetized version of the structure can be created. Remotely sensed data tends to focus on nadir or near nadir imagery while trying to minimize overlap in order to achieve the greatest ground coverage possible during a data collection. A workflow is being developed at Digital Imaging and Remote Sensing (DIRS) Group at the Rochester Institute of Technology (RIT) that utilizes these phototourism techniques, which typically use dense coverage of a small object or region, and applies them to remotely sensed imagery, which involves sparse data coverage of a large area. In addition to this, RIT has planned and executed a high-overlap image collection, using the RIT WASP system, to study the requirements needed for such three-dimensional reconstruction efforts. While the collection was extensive, the intention was to find the minimum number of images and frame overlap needed to generate quality point clouds. This paper will discuss the image data collection effort and what it means to generate and evaluate a quality point cloud for reconstruction purposes.
Recent Development of Dual-Dictionary Learning Approach in Medical Image Analysis and Reconstruction.
Wang, Bigong; Li, Liang
As an implementation of compressive sensing (CS), dual-dictionary learning (DDL) method provides an ideal access to restore signals of two related dictionaries and sparse representation. It has been proven that this method performs well in medical image reconstruction with highly undersampled data, especially for multimodality imaging like CT-MRI hybrid reconstruction. Because of its outstanding strength, short signal acquisition time, and low radiation dose, DDL has allured a broad interest in both academic and industrial fields. Here in this review article, we summarize DDL's development history, conclude the latest advance, and also discuss its role in the future directions and potential applications in medical imaging. Meanwhile, this paper points out that DDL is still in the initial stage, and it is necessary to make further studies to improve this method, especially in dictionary training.
A Sparse Bayesian Imaging Technique for Efficient Recovery of Reservoir Channels With Time-Lapse Seismic Measurements
Subsurface reservoir flow channels are characterized by high-permeability values and serve as preferred pathways for fluid propagation. Accurate estimation of their geophysical structures is thus of great importance for the oil industry. The ensemble Kalman filter (EnKF) is a widely used statistical technique for estimating subsurface reservoir model parameters. However, accurate reconstruction of the subsurface geological features with the EnKF is challenging because of the limited measurements available from the wells and the smoothing effects imposed by the \\\\ell _{2} -norm nature of its update step. A new EnKF scheme based on sparse domain representation was introduced by Sana et al. (2015) to incorporate useful prior structural information in the estimation process for efficient recovery of subsurface channels. In this paper, we extend this work in two ways: 1) investigate the effects of incorporating time-lapse seismic data on the channel reconstruction; and 2) explore a Bayesian sparse reconstruction algorithm with the potential ability to reduce the computational requirements. Numerical results suggest that the performance of the new sparse Bayesian based EnKF scheme is enhanced with the availability of seismic measurements, leading to further improvement in the recovery of flow channels structures. The sparse Bayesian approach further provides a computationally efficient framework for enforcing a sparse solution, especially with the possibility of using high sparsity rates through the inclusion of seismic data.
Sparse coded image super-resolution using K-SVD trained dictionary based on regularized orthogonal matching pursuit.
Sajjad, Muhammad; Mehmood, Irfan; Baik, Sung Wook
Image super-resolution (SR) plays a vital role in medical imaging that allows a more efficient and effective diagnosis process. Usually, diagnosing is difficult and inaccurate from low-resolution (LR) and noisy images. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps, such as segmentation and registration. Therefore, we propose an efficient sparse coded image SR reconstruction technique using a trained dictionary. We apply a simple and efficient regularized version of orthogonal matching pursuit (ROMP) to seek the coefficients of sparse representation. ROMP has the transparency and greediness of OMP and the robustness of the L1-minization that enhance the dictionary learning process to capture feature descriptors such as oriented edges and contours from complex images like brain MRIs. The sparse coding part of the K-SVD dictionary training procedure is modified by substituting OMP with ROMP. The dictionary update stage allows simultaneously updating an arbitrary number of atoms and vectors of sparse coefficients. In SR reconstruction, ROMP is used to determine the vector of sparse coefficients for the underlying patch. The recovered representations are then applied to the trained dictionary, and finally, an optimization leads to high-resolution output of high-quality. Experimental results demonstrate that the super-resolution reconstruction quality of the proposed scheme is comparatively better than other state-of-the-art schemes.
Sana, Furrukh; Ravanelli, Fabio; Al-Naffouri, Tareq Y.; Hoteit, Ibrahim
Subsurface reservoir flow channels are characterized by high-permeability values and serve as preferred pathways for fluid propagation. Accurate estimation of their geophysical structures is thus of great importance for the oil industry. The ensemble Kalman filter (EnKF) is a widely used statistical technique for estimating subsurface reservoir model parameters. However, accurate reconstruction of the subsurface geological features with the EnKF is challenging because of the limited measurements available from the wells and the smoothing effects imposed by the \\ell _{2} -norm nature of its update step. A new EnKF scheme based on sparse domain representation was introduced by Sana et al. (2015) to incorporate useful prior structural information in the estimation process for efficient recovery of subsurface channels. In this paper, we extend this work in two ways: 1) investigate the effects of incorporating time-lapse seismic data on the channel reconstruction; and 2) explore a Bayesian sparse reconstruction algorithm with the potential ability to reduce the computational requirements. Numerical results suggest that the performance of the new sparse Bayesian based EnKF scheme is enhanced with the availability of seismic measurements, leading to further improvement in the recovery of flow channels structures. The sparse Bayesian approach further provides a computationally efficient framework for enforcing a sparse solution, especially with the possibility of using high sparsity rates through the inclusion of seismic data.
Precise RFID localization in impaired environment through sparse signal recovery
Subedi, Saurav; Zhang, Yimin D.; Amin, Moeness G.
Radio frequency identification (RFID) is a rapidly developing wireless communication technology for electronically identifying, locating, and tracking products, assets, and personnel. RFID has become one of the most important means to construct real-time locating systems (RTLS) that track and identify the location of objects in real time using simple, inexpensive tags and readers. The applicability and usefulness of RTLS techniques depend on their achievable accuracy. In particular, when multilateration-based localization techniques are exploited, the achievable accuracy primarily relies on the precision of the range estimates between a reader and the tags. Such range information can be obtained by using the received signal strength indicator (RSSI) and/or the phase difference of arrival (PDOA). In both cases, however, the accuracy is significantly compromised when the operation environment is impaired. In particular, multipath propagation significantly affects the measurement accuracy of both RSSI and phase information. In addition, because RFID systems are typically operated in short distances, RSSI and phase measurements are also coupled with the reader and tag antenna patterns, making accurate RFID localization very complicated and challenging. In this paper, we develop new methods to localize RFID tags or readers by exploiting sparse signal recovery techniques. The proposed method allows the channel environment and antenna patterns to be taken into account and be properly compensated at a low computational cost. As such, the proposed technique yields superior performance in challenging operation environments with the above-mentioned impairments.
3D dictionary learning based iterative cone beam CT reconstruction
Ti Bai
Full Text Available Purpose: This work is to develop a 3D dictionary learning based cone beam CT (CBCT reconstruction algorithm on graphic processing units (GPU to improve the quality of sparse-view CBCT reconstruction with high efficiency. Methods: A 3D dictionary containing 256 small volumes (atoms of 3 × 3 × 3 was trained from a large number of blocks extracted from a high quality volume image. On the basis, we utilized cholesky decomposition based orthogonal matching pursuit algorithm to find the sparse representation of each block. To accelerate the time-consuming sparse coding in the 3D case, we implemented the sparse coding in a parallel fashion by taking advantage of the tremendous computational power of GPU. Conjugate gradient least square algorithm was adopted to minimize the data fidelity term. Evaluations are performed based on a head-neck patient case. FDK reconstruction with full dataset of 364 projections is used as the reference. We compared the proposed 3D dictionary learning based method with tight frame (TF by performing reconstructions on a subset data of 121 projections. Results: Compared to TF based CBCT reconstruction that shows good overall performance, our experiments indicated that 3D dictionary learning based CBCT reconstruction is able to recover finer structures, remove more streaking artifacts and also induce less blocky artifacts. Conclusion: 3D dictionary learning based CBCT reconstruction algorithm is able to sense the structural information while suppress the noise, and hence to achieve high quality reconstruction under the case of sparse view. The GPU realization of the whole algorithm offers a significant efficiency enhancement, making this algorithm more feasible for potential clinical application.-------------------------------Cite this article as: Bai T, Yan H, Shi F, Jia X, Lou Y, Xu Q, Jiang S, Mou X. 3D dictionary learning based iterative cone beam CT reconstruction. Int J Cancer Ther Oncol 2014; 2(2:020240. DOI: 10
Jørgensen, Jakob S.; Coban, Sophia B.; Lionheart, William R. B.; McDonald, Samuel A.; Withers, Philip J.
Sparsity regularization (SR) such as total variation (TV) minimization allows accurate image reconstruction in x-ray computed tomography (CT) from fewer projections than analytical methods. Exactly how few projections suffice and how this number may depend on the image remain poorly understood. Compressive sensing connects the critical number of projections to the image sparsity, but does not cover CT, however empirical results suggest a similar connection. The present work establishes for real CT data a connection between gradient sparsity and the sufficient number of projections for accurate TV-regularized reconstruction. A collection of 48 x-ray CT datasets called SparseBeads was designed for benchmarking SR reconstruction algorithms. Beadpacks comprising glass beads of five different sizes as well as mixtures were scanned in a micro-CT scanner to provide structured datasets with variable image sparsity levels, number of projections and noise levels to allow the systematic assessment of parameters affecting performance of SR reconstruction algorithms6. Using the SparseBeads data, TV-regularized reconstruction quality was assessed as a function of numbers of projections and gradient sparsity. The critical number of projections for satisfactory TV-regularized reconstruction increased almost linearly with the gradient sparsity. This establishes a quantitative guideline from which one may predict how few projections to acquire based on expected sample sparsity level as an aid in planning of dose- or time-critical experiments. The results are expected to hold for samples of similar characteristics, i.e. consisting of few, distinct phases with relatively simple structure. Such cases are plentiful in porous media, composite materials, foams, as well as non-destructive testing and metrology. For samples of other characteristics the proposed methodology may be used to investigate similar relations.
Novel criteria of uniqueness for signal reconstruction from phase
Ma, C.
An approach for ascertaining whether a signal is uniquely determined by its Fourier transform phase is proposed. It is shown that uniqueness corresponds to the nonsingularity of a matrix which can be formed from the finite-length real sequence. The criterion of uniqueness for reconstructing a
Large-region acoustic source mapping using a movable array and sparse covariance fitting.
Zhao, Shengkui; Tuna, Cagdas; Nguyen, Thi Ngoc Tho; Jones, Douglas L
Large-region acoustic source mapping is important for city-scale noise monitoring. Approaches using a single-position measurement scheme to scan large regions using small arrays cannot provide clean acoustic source maps, while deploying large arrays spanning the entire region of interest is prohibitively expensive. A multiple-position measurement scheme is applied to scan large regions at multiple spatial positions using a movable array of small size. Based on the multiple-position measurement scheme, a sparse-constrained multiple-position vectorized covariance matrix fitting approach is presented. In the proposed approach, the overall sample covariance matrix of the incoherent virtual array is first estimated using the multiple-position array data and then vectorized using the Khatri-Rao (KR) product. A linear model is then constructed for fitting the vectorized covariance matrix and a sparse-constrained reconstruction algorithm is proposed for recovering source powers from the model. The user parameter settings are discussed. The proposed approach is tested on a 30 m × 40 m region and a 60 m × 40 m region using simulated and measured data. Much cleaner acoustic source maps and lower sound pressure level errors are obtained compared to the beamforming approaches and the previous sparse approach [Zhao, Tuna, Nguyen, and Jones, Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP) (2016)].
An approach to reconstruction of a natural crack using signals of eddy current testing. 1. Reconstruction of an idealized natural crack
Chen, Zhenmao
In this paper, an approach to the reconstruction of an idealized natural crack of non-vanishing conductivity is proposed with use of signals of eddy current testing. Two numerical models are introduced at first for modeling a Stress Corrosion Crack (SCC) in order it possibly to be represented by a set of crack parameters. A method for rapid prediction of the eddy current testing signals arisen from these idealized cracks is given then by extending a knowledge based fast forward solver developed by authors to the case of a non-vanishing conductivity. On the other hand, the inverse algorithm of conjugate gradient method is improved to reconstruct the crack parameters and is implemented with the pick-up signals and gradients calculated by using the rapid forward solver. Several examples are presented finally for validating the proposed strategy. The results verified that both of the models can give reasonable reconstruction results in case of a low noise level. The model concerning the touch of crack surfaces with a conducting band region surrounded by the crack edge, however, is proved more efficient that the model using a conductivity distribution from the point of view of both reconstruction speed and accuracy. (author)
A Sparse Auto Encoder Deep Process Neural Network Model and its Application
Xu Shaohua
Full Text Available Aiming at the problem of time-varying signal pattern classification, a sparse auto-encoder deep process neural network (SAE-DPNN is proposed. The input of SAE-DPNN is time-varying process signal and the output is pattern category. It combines the time-varying signal classification method of process neural network (PNN and the data feature extraction and hierarchical sparse representation mechanism of sparse automatic encoder (SAE. Based on the feedforward PNN model, SAE-DPNN is constructed by stacking the process neurons, SAE network and softmax classifier. It can maintain the time-sequence and structure of the input signal, express and synthesize the process distribution characteristics of multidimensional time-varying signals and their combinations. SAE-DPNN improves the identification of complex features and distinguishes between different types of signals, realizes the direct classification of time-varying signals. In this paper, the feature extraction and representation mechanism of time-varying signal in SAE-DPNN are analyzed, and a specific learning algorithm is given. The experimental results verify the effectiveness of the model and algorithm.
Sparse Representation Based SAR Vehicle Recognition along with Aspect Angle
Xiangwei Xing
Full Text Available As a method of representing the test sample with few training samples from an overcomplete dictionary, sparse representation classification (SRC has attracted much attention in synthetic aperture radar (SAR automatic target recognition (ATR recently. In this paper, we develop a novel SAR vehicle recognition method based on sparse representation classification along with aspect information (SRCA, in which the correlation between the vehicle's aspect angle and the sparse representation vector is exploited. The detailed procedure presented in this paper can be summarized as follows. Initially, the sparse representation vector of a test sample is solved by sparse representation algorithm with a principle component analysis (PCA feature-based dictionary. Then, the coefficient vector is projected onto a sparser one within a certain range of the vehicle's aspect angle. Finally, the vehicle is classified into a certain category that minimizes the reconstruction error with the novel sparse representation vector. Extensive experiments are conducted on the moving and stationary target acquisition and recognition (MSTAR dataset and the results demonstrate that the proposed method performs robustly under the variations of depression angle and target configurations, as well as incomplete observation.
Sample selection based on kernel-subclustering for the signal reconstruction of multifunctional sensors
Wang, Xin; Wei, Guo; Sun, Jinwei
The signal reconstruction methods based on inverse modeling for the signal reconstruction of multifunctional sensors have been widely studied in recent years. To improve the accuracy, the reconstruction methods have become more and more complicated because of the increase in the model parameters and sample points. However, there is another factor that affects the reconstruction accuracy, the position of the sample points, which has not been studied. A reasonable selection of the sample points could improve the signal reconstruction quality in at least two ways: improved accuracy with the same number of sample points or the same accuracy obtained with a smaller number of sample points. Both ways are valuable for improving the accuracy and decreasing the workload, especially for large batches of multifunctional sensors. In this paper, we propose a sample selection method based on kernel-subclustering distill groupings of the sample data and produce the representation of the data set for inverse modeling. The method calculates the distance between two data points based on the kernel-induced distance instead of the conventional distance. The kernel function is a generalization of the distance metric by mapping the data that are non-separable in the original space into homogeneous groups in the high-dimensional space. The method obtained the best results compared with the other three methods in the simulation. (paper)
Effect of Hadron Contamination on Dielectron Signal Reconstruction in Heavy Flavor Production Measurements
Kikoła, Daniel
Dielectron signal reconstruction is an important tool for heavy flavor measurements because of its trigger feasibility and its relatively straightforward particle identification process. However, in the case of time projection chamber detectors, some hadron contamination is unavoidable, even if additional means are used to improve the particle identification process. In this paper, we investigate the effects of hadron (protons, pions, and kaons) contamination on the dielectron signal reconstruction process in the measurement of J/ψ and electrons from heavy flavor hadron decays
Recent Development of Dual-Dictionary Learning Approach in Medical Image Analysis and Reconstruction
As an implementation of compressive sensing (CS), dual-dictionary learning (DDL) method provides an ideal access to restore signals of two related dictionaries and sparse representation. It has been proven that this method performs well in medical image reconstruction with highly undersampled data, especially for multimodality imaging like CT-MRI hybrid reconstruction. Because of its outstanding strength, short signal acquisition time, and low radiation dose, DDL has allured a broad interest in both academic and industrial fields. Here in this review article, we summarize DDL's development history, conclude the latest advance, and also discuss its role in the future directions and potential applications in medical imaging. Meanwhile, this paper points out that DDL is still in the initial stage, and it is necessary to make further studies to improve this method, especially in dictionary training. PMID:26089956
Separation and reconstruction of high pressure water-jet reflective sound signal based on ICA
Yang, Hongtao; Sun, Yuling; Li, Meng; Zhang, Dongsu; Wu, Tianfeng
The impact of high pressure water-jet on the different materials target will produce different reflective mixed sound. In order to reconstruct the reflective sound signals distribution on the linear detecting line accurately and to separate the environment noise effectively, the mixed sound signals acquired by linear mike array were processed by ICA. The basic principle of ICA and algorithm of FASTICA were described in detail. The emulation experiment was designed. The environment noise signal was simulated by using band-limited white noise and the reflective sound signal was simulated by using pulse signal. The reflective sound signal attenuation produced by the different distance transmission was simulated by weighting the sound signal with different contingencies. The mixed sound signals acquired by linear mike array were synthesized by using the above simulated signals and were whitened and separated by ICA. The final results verified that the environment noise separation and the reconstruction of the detecting-line sound distribution can be realized effectively.
Sparse Matrix for ECG Identification with Two-Lead Features
Kuo-Kun Tseng
Full Text Available Electrocardiograph (ECG human identification has the potential to improve biometric security. However, improvements in ECG identification and feature extraction are required. Previous work has focused on single lead ECG signals. Our work proposes a new algorithm for human identification by mapping two-lead ECG signals onto a two-dimensional matrix then employing a sparse matrix method to process the matrix. And that is the first application of sparse matrix techniques for ECG identification. Moreover, the results of our experiments demonstrate the benefits of our approach over existing methods.
Sparse Vector Distributions and Recovery from Compressed Sensing
Sturm, Bob L.
It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I...... empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two morals of this work are: 1) any judgement of the recovery performance of one algorithm over that of another must be prefaced by the conditions for which this is observed to be true, including sparse vector...... distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal....
The w-effect in interferometric imaging: from a fast sparse measurement operator to superresolution
Dabbech, A.; Wolz, L.; Pratley, L.; McEwen, J. D.; Wiaux, Y.
Modern radio telescopes, such as the Square Kilometre Array, will probe the radio sky over large fields of view, which results in large w-modulations of the sky image. This effect complicates the relationship between the measured visibilities and the image under scrutiny. In algorithmic terms, it gives rise to massive memory and computational time requirements. Yet, it can be a blessing in terms of reconstruction quality of the sky image. In recent years, several works have shown that large w-modulations promote the spread spectrum effect. Within the compressive sensing framework, this effect increases the incoherence between the sensing basis and the sparsity basis of the signal to be recovered, leading to better estimation of the sky image. In this article, we revisit the w-projection approach using convex optimization in realistic settings, where the measurement operator couples the w-terms in Fourier and the de-gridding kernels. We provide sparse, thus fast, models of the Fourier part of the measurement operator through adaptive sparsification procedures. Consequently, memory requirements and computational cost are significantly alleviated at the expense of introducing errors on the radio interferometric data model. We present a first investigation of the impact of the sparse variants of the measurement operator on the image reconstruction quality. We finally analyse the interesting superresolution potential associated with the spread spectrum effect of the w-modulation, and showcase it through simulations. Our c++ code is available online on GitHub.
Dictionary-based image reconstruction for superresolution in integrated circuit imaging.
Cilingiroglu, T Berkin; Uyar, Aydan; Tuysuzoglu, Ahmet; Karl, W Clem; Konrad, Janusz; Goldberg, Bennett B; Ünlü, M Selim
Resolution improvement through signal processing techniques for integrated circuit imaging is becoming more crucial as the rapid decrease in integrated circuit dimensions continues. Although there is a significant effort to push the limits of optical resolution for backside fault analysis through the use of solid immersion lenses, higher order laser beams, and beam apodization, signal processing techniques are required for additional improvement. In this work, we propose a sparse image reconstruction framework which couples overcomplete dictionary-based representation with a physics-based forward model to improve resolution and localization accuracy in high numerical aperture confocal microscopy systems for backside optical integrated circuit analysis. The effectiveness of the framework is demonstrated on experimental data.
Multicore Performance of Block Algebraic Iterative Reconstruction Methods
Sørensen, Hans Henrik B.; Hansen, Per Christian
Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely on semiconv......Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely...... on semiconvergence. Block versions of these methods, based on a partitioning of the linear system, are able to combine the fast semiconvergence of ART with the better multicore properties of SIRT. These block methods separate into two classes: those that, in each iteration, access the blocks in a sequential manner...... a fixed relaxation parameter in each method, namely, the one that leads to the fastest semiconvergence. Computational results show that for multicore computers, the sequential approach is preferable....
Sparsity-promoting orthogonal dictionary updating for image reconstruction from highly undersampled magnetic resonance data
Huang, Jinhong; Guo, Li; Feng, Qianjin; Chen, Wufan; Feng, Yanqiu
Image reconstruction from undersampled k-space data accelerates magnetic resonance imaging (MRI) by exploiting image sparseness in certain transform domains. Employing image patch representation over a learned dictionary has the advantage of being adaptive to local image structures and thus can better sparsify images than using fixed transforms (e.g. wavelets and total variations). Dictionary learning methods have recently been introduced to MRI reconstruction, and these methods demonstrate significantly reduced reconstruction errors compared to sparse MRI reconstruction using fixed transforms. However, the synthesis sparse coding problem in dictionary learning is NP-hard and computationally expensive. In this paper, we present a novel sparsity-promoting orthogonal dictionary updating method for efficient image reconstruction from highly undersampled MRI data. The orthogonality imposed on the learned dictionary enables the minimization problem in the reconstruction to be solved by an efficient optimization algorithm which alternately updates representation coefficients, orthogonal dictionary, and missing k-space data. Moreover, both sparsity level and sparse representation contribution using updated dictionaries gradually increase during iterations to recover more details, assuming the progressively improved quality of the dictionary. Simulation and real data experimental results both demonstrate that the proposed method is approximately 10 to 100 times faster than the K-SVD-based dictionary learning MRI method and simultaneously improves reconstruction accuracy. (paper)
Sparsity-promoting orthogonal dictionary updating for image reconstruction from highly undersampled magnetic resonance data.
Image reconstruction from undersampled k-space data accelerates magnetic resonance imaging (MRI) by exploiting image sparseness in certain transform domains. Employing image patch representation over a learned dictionary has the advantage of being adaptive to local image structures and thus can better sparsify images than using fixed transforms (e.g. wavelets and total variations). Dictionary learning methods have recently been introduced to MRI reconstruction, and these methods demonstrate significantly reduced reconstruction errors compared to sparse MRI reconstruction using fixed transforms. However, the synthesis sparse coding problem in dictionary learning is NP-hard and computationally expensive. In this paper, we present a novel sparsity-promoting orthogonal dictionary updating method for efficient image reconstruction from highly undersampled MRI data. The orthogonality imposed on the learned dictionary enables the minimization problem in the reconstruction to be solved by an efficient optimization algorithm which alternately updates representation coefficients, orthogonal dictionary, and missing k-space data. Moreover, both sparsity level and sparse representation contribution using updated dictionaries gradually increase during iterations to recover more details, assuming the progressively improved quality of the dictionary. Simulation and real data experimental results both demonstrate that the proposed method is approximately 10 to 100 times faster than the K-SVD-based dictionary learning MRI method and simultaneously improves reconstruction accuracy.
Superresolving Black Hole Images with Full-Closure Sparse Modeling
Crowley, Chelsea; Akiyama, Kazunori; Fish, Vincent
It is believed that almost all galaxies have black holes at their centers. Imaging a black hole is a primary objective to answer scientific questions relating to relativistic accretion and jet formation. The Event Horizon Telescope (EHT) is set to capture images of two nearby black holes, Sagittarius A* at the center of the Milky Way galaxy roughly 26,000 light years away and the other M87 which is in Virgo A, a large elliptical galaxy that is 50 million light years away. Sparse imaging techniques have shown great promise for reconstructing high-fidelity superresolved images of black holes from simulated data. Previous work has included the effects of atmospheric phase errors and thermal noise, but not systematic amplitude errors that arise due to miscalibration. We explore a full-closure imaging technique with sparse modeling that uses closure amplitudes and closure phases to improve the imaging process. This new technique can successfully handle data with systematic amplitude errors. Applying our technique to synthetic EHT data of M87, we find that full-closure sparse modeling can reconstruct images better than traditional methods and recover key structural information on the source, such as the shape and size of the predicted photon ring. These results suggest that our new approach will provide superior imaging performance for data from the EHT and other interferometric arrays.
Coronary endothelial function assessment using self-gated cardiac cine MRI and k-t sparse SENSE.
Yerly, Jérôme; Ginami, Giulia; Nordio, Giovanna; Coristine, Andrew J; Coppo, Simone; Monney, Pierre; Stuber, Matthias
Electrocardiogram (ECG)-gated cine MRI, paired with isometric handgrip exercise, can be used to accurately, reproducibly, and noninvasively measure coronary endothelial function (CEF). Obtaining a reliable ECG signal at higher field strengths, however, can be challenging due to rapid gradient switching and an increased heart rate under stress. To address these limitations, we present a self-gated cardiac cine MRI framework for CEF measurements that operates without ECG signal. Cross-sectional slices of the right coronary artery (RCA) were acquired using a two-dimensional golden angle radial trajectory. This sampling approach, combined with the k-t sparse SENSE algorithm, allows for the reconstruction of both real-time images for self-gating signal calculations and retrospectively reordered self-gated cine images. CEF measurements were quantitatively compared using both the self-gated and the standard ECG-gated approach. Self-gated cine images with high-quality, temporal, and spatial resolution were reconstructed for 18 healthy volunteers. CEF as measured in self-gated images was in good agreement (R 2  = 0.60) with that measured by its standard ECG-gated counterpart. High spatial and temporal resolution cross-sectional cine images of the RCA can be obtained without ECG signal. The coronary vasomotor response to handgrip exercise compares favorably with that obtained with the standard ECG-gated method. Magn Reson Med 76:1443-1454, 2015. © 2015 International Society for Magnetic Resonance in Medicine. © 2015 International Society for Magnetic Resonance in Medicine.
Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.
Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli
Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.
Duplex scanning using sparse data sequences
Møllenbach, S. K.; Jensen, Jørgen Arendt
reconstruction of the missing samples possible. The periodic pattern has the length T = M + A samples, where M are for B-mode and A for velocity estimation. The missing samples can now be reconstructed using a filter bank. One filter bank reconstructs one missing sample, so the number of filter banks corresponds...... to M. The number of sub filters in every filter bank is the same as A. Every sub filter contains fractional delay (FD) filter and an interpolation function. Many different sequences can be selected to adapt the B-mode frame rate needed. The drawback of the method is that the maximum velocity detectable......, the fprf and the resolution are 15 MHz, 3.5 kHz, and 12 bit sample (8 kHz and 16 bit for the Carotid artery). The resulting data contains 8000 RF lines with 128 samples at a depth of 45 mm for the vein and 50 mm for Aorta. Sparse sequences are constructed from the full data sequences to have both...
Real-time cardiac magnetic resonance cine imaging with sparse sampling and iterative reconstruction for left-ventricular measures: Comparison with gold-standard segmented steady-state free precession.
Camargo, Gabriel C; Erthal, Fernanda; Sabioni, Leticia; Penna, Filipe; Strecker, Ralph; Schmidt, Michaela; Zenge, Michael O; Lima, Ronaldo de S L; Gottlieb, Ilan
Segmented cine imaging with a steady-state free-precession sequence (Cine-SSFP) is currently the gold standard technique for measuring ventricular volumes and mass, but due to multi breath-hold (BH) requirements, it is prone to misalignment of consecutive slices, time consuming and dependent on respiratory capacity. Real-time cine avoids those limitations, but poor spatial and temporal resolution of conventional sequences has prevented its routine application. We sought to examine the accuracy and feasibility of a newly developed real-time sequence with aggressive under-sampling of k-space using sparse sampling and iterative reconstruction (Cine-RT). Stacks of short-axis cines were acquired covering both ventricles in a 1.5T system using gold standard Cine-SSFP and Cine-RT. Acquisition parameters for Cine-SSFP were: acquisition matrix of 224×196, temporal resolution of 39ms, retrospective gating, with an average of 8 heartbeats per slice and 1-2 slices/BH. For Cine-RT: acquisition matrix of 224×196, sparse sampling net acceleration factor of 11.3, temporal resolution of 41ms, prospective gating, real-time acquisition of 1 heart-beat/slice and all slices in one BH. LV contours were drawn at end diastole and systole to derive LV volumes and mass. Forty-one consecutive patients (15 male; 41±17years) in sinus rhythm were successfully included. All images from Cine-SSFP and Cine-RT were considered to have excellent quality. Cine-RT-derived LV volumes and mass were slightly underestimated but strongly correlated with gold standard Cine-SSFP. Inter- and intra-observer analysis presented similar results between both sequences. Cine-RT featuring sparse sampling and iterative reconstruction can achieve spatial and temporal resolution equivalent to Cine-SSFP, providing excellent image quality, with similar precision measurements and highly correlated and only slightly underestimated volume and mass values. Copyright © 2017 Elsevier Inc. All rights reserved.
Shape prior modeling using sparse representation and online dictionary learning.
Zhang, Shaoting; Zhan, Yiqiang; Zhou, Yan; Uzunbas, Mustafa; Metaxas, Dimitris N
The recently proposed sparse shape composition (SSC) opens a new avenue for shape prior modeling. Instead of assuming any parametric model of shape statistics, SSC incorporates shape priors on-the-fly by approximating a shape instance (usually derived from appearance cues) by a sparse combination of shapes in a training repository. Theoretically, one can increase the modeling capability of SSC by including as many training shapes in the repository. However, this strategy confronts two limitations in practice. First, since SSC involves an iterative sparse optimization at run-time, the more shape instances contained in the repository, the less run-time efficiency SSC has. Therefore, a compact and informative shape dictionary is preferred to a large shape repository. Second, in medical imaging applications, training shapes seldom come in one batch. It is very time consuming and sometimes infeasible to reconstruct the shape dictionary every time new training shapes appear. In this paper, we propose an online learning method to address these two limitations. Our method starts from constructing an initial shape dictionary using the K-SVD algorithm. When new training shapes come, instead of re-constructing the dictionary from the ground up, we update the existing one using a block-coordinates descent approach. Using the dynamically updated dictionary, sparse shape composition can be gracefully scaled up to model shape priors from a large number of training shapes without sacrificing run-time efficiency. Our method is validated on lung localization in X-Ray and cardiac segmentation in MRI time series. Compared to the original SSC, it shows comparable performance while being significantly more efficient.
Sparse RNA folding revisited: space-efficient minimum free energy structure prediction.
Will, Sebastian; Jabbari, Hosna
RNA secondary structure prediction by energy minimization is the central computational tool for the analysis of structural non-coding RNAs and their interactions. Sparsification has been successfully applied to improve the time efficiency of various structure prediction algorithms while guaranteeing the same result; however, for many such folding problems, space efficiency is of even greater concern, particularly for long RNA sequences. So far, space-efficient sparsified RNA folding with fold reconstruction was solved only for simple base-pair-based pseudo-energy models. Here, we revisit the problem of space-efficient free energy minimization. Whereas the space-efficient minimization of the free energy has been sketched before, the reconstruction of the optimum structure has not even been discussed. We show that this reconstruction is not possible in trivial extension of the method for simple energy models. Then, we present the time- and space-efficient sparsified free energy minimization algorithm SparseMFEFold that guarantees MFE structure prediction. In particular, this novel algorithm provides efficient fold reconstruction based on dynamically garbage-collected trace arrows. The complexity of our algorithm depends on two parameters, the number of candidates Z and the number of trace arrows T; both are bounded by [Formula: see text], but are typically much smaller. The time complexity of RNA folding is reduced from [Formula: see text] to [Formula: see text]; the space complexity, from [Formula: see text] to [Formula: see text]. Our empirical results show more than 80 % space savings over RNAfold [Vienna RNA package] on the long RNAs from the RNA STRAND database (≥2500 bases). The presented technique is intentionally generalizable to complex prediction algorithms; due to their high space demands, algorithms like pseudoknot prediction and RNA-RNA-interaction prediction are expected to profit even stronger than "standard" MFE folding. SparseMFEFold is free
A tensor-based dictionary learning approach to tomographic image reconstruction
Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion...... coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem...... with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images...
Feature reconstruction of LFP signals based on PLSR in the neural information decoding study.
Yonghui Dong; Zhigang Shang; Mengmeng Li; Xinyu Liu; Hong Wan
To solve the problems of Signal-to-Noise Ratio (SNR) and multicollinearity when the Local Field Potential (LFP) signals is used for the decoding of animal motion intention, a feature reconstruction of LFP signals based on partial least squares regression (PLSR) in the neural information decoding study is proposed in this paper. Firstly, the feature information of LFP coding band is extracted based on wavelet transform. Then the PLSR model is constructed by the extracted LFP coding features. According to the multicollinearity characteristics among the coding features, several latent variables which contribute greatly to the steering behavior are obtained, and the new LFP coding features are reconstructed. Finally, the K-Nearest Neighbor (KNN) method is used to classify the reconstructed coding features to verify the decoding performance. The results show that the proposed method can achieve the highest accuracy compared to the other three methods and the decoding effect of the proposed method is robust.
Multiple Kernel Sparse Representation based Orthogonal Discriminative Projection and Its Cost-Sensitive Extension.
Zhang, Guoqing; Sun, Huaijiang; Xia, Guiyu; Sun, Quansen
Sparse representation based classification (SRC) has been developed and shown great potential for real-world application. Based on SRC, Yang et al. [10] devised a SRC steered discriminative projection (SRC-DP) method. However, as a linear algorithm, SRC-DP cannot handle the data with highly nonlinear distribution. Kernel sparse representation-based classifier (KSRC) is a non-linear extension of SRC and can remedy the drawback of SRC. KSRC requires the use of a predetermined kernel function and selection of the kernel function and its parameters is difficult. Recently, multiple kernel learning for SRC (MKL-SRC) [22] has been proposed to learn a kernel from a set of base kernels. However, MKL-SRC only considers the within-class reconstruction residual while ignoring the between-class relationship, when learning the kernel weights. In this paper, we propose a novel multiple kernel sparse representation-based classifier (MKSRC), and then we use it as a criterion to design a multiple kernel sparse representation based orthogonal discriminative projection method (MK-SR-ODP). The proposed algorithm aims at learning a projection matrix and a corresponding kernel from the given base kernels such that in the low dimension subspace the between-class reconstruction residual is maximized and the within-class reconstruction residual is minimized. Furthermore, to achieve a minimum overall loss by performing recognition in the learned low-dimensional subspace, we introduce cost information into the dimensionality reduction method. The solutions for the proposed method can be efficiently found based on trace ratio optimization method [33]. Extensive experimental results demonstrate the superiority of the proposed algorithm when compared with the state-of-the-art methods.
SparseM: A Sparse Matrix Package for R *
Roger Koenker
Full Text Available SparseM provides some basic R functionality for linear algebra with sparse matrices. Use of the package is illustrated by a family of linear model fitting functions that implement least squares methods for problems with sparse design matrices. Significant performance improvements in memory utilization and computational speed are possible for applications involving large sparse matrices.
Compressive sensing-based electrostatic sensor array signal processing and exhausted abnormal debris detecting
Tang, Xin; Chen, Zhongsheng; Li, Yue; Yang, Yongmin
When faults happen at gas path components of gas turbines, some sparsely-distributed and charged debris will be generated and released into the exhaust gas. The debris is called abnormal debris. Electrostatic sensors can detect the debris online and further indicate the faults. It is generally considered that, under a specific working condition, a more serious fault generates more and larger debris, and a piece of larger debris carries more charge. Therefore, the amount and charge of the abnormal debris are important indicators of the fault severity. However, because an electrostatic sensor can only detect the superposed effect on the electrostatic field of all the debris, it can hardly identify the amount and position of the debris. Moreover, because signals of electrostatic sensors depend on not only charge but also position of debris, and the position information is difficult to acquire, measuring debris charge accurately using the electrostatic detecting method is still a technical difficulty. To solve these problems, a hemisphere-shaped electrostatic sensors' circular array (HSESCA) is used, and an array signal processing method based on compressive sensing (CS) is proposed in this paper. To research in a theoretical framework of CS, the measurement model of the HSESCA is discretized into a sparse representation form by meshing. In this way, the amount and charge of the abnormal debris are described as a sparse vector. It is further reconstructed by constraining l1-norm when solving an underdetermined equation. In addition, a pre-processing method based on singular value decomposition and a result calibration method based on weighted-centroid algorithm are applied to ensure the accuracy of the reconstruction. The proposed method is validated by both numerical simulations and experiments. Reconstruction errors, characteristics of the results and some related factors are discussed.
Constrained Convolutional Sparse Coding for Parametric Based Reconstruction of Line Drawings
Shaheen, Sara
Convolutional sparse coding (CSC) plays an essential role in many computer vision applications ranging from image compression to deep learning. In this work, we spot the light on a new application where CSC can effectively serve, namely line drawing analysis. The process of drawing a line drawing can be approximated as the sparse spatial localization of a number of typical basic strokes, which in turn can be cast as a non-standard CSC model that considers the line drawing formation process from parametric curves. These curves are learned to optimize the fit between the model and a specific set of line drawings. Parametric representation of sketches is vital in enabling automatic sketch analysis, synthesis and manipulation. A couple of sketch manipulation examples are demonstrated in this work. Consequently, our novel method is expected to provide a reliable and automatic method for parametric sketch description. Through experiments, we empirically validate the convergence of our method to a feasible solution.
A Non-Uniformly Under-Sampled Blade Tip-Timing Signal Reconstruction Method for Blade Vibration Monitoring
Zheng Hu
Full Text Available High-speed blades are often prone to fatigue due to severe blade vibrations. In particular, synchronous vibrations can cause irreversible damages to the blade. Blade tip-timing methods (BTT have become a promising way to monitor blade vibrations. However, synchronous vibrations are unsuitably monitored by uniform BTT sampling. Therefore, non-equally mounted probes have been used, which will result in the non-uniformity of the sampling signal. Since under-sampling is an intrinsic drawback of BTT methods, how to analyze non-uniformly under-sampled BTT signals is a big challenge. In this paper, a novel reconstruction method for non-uniformly under-sampled BTT data is presented. The method is based on the periodically non-uniform sampling theorem. Firstly, a mathematical model of a non-uniform BTT sampling process is built. It can be treated as the sum of certain uniform sample streams. For each stream, an interpolating function is required to prevent aliasing in the reconstructed signal. Secondly, simultaneous equations of all interpolating functions in each sub-band are built and corresponding solutions are ultimately derived to remove unwanted replicas of the original signal caused by the sampling, which may overlay the original signal. In the end, numerical simulations and experiments are carried out to validate the feasibility of the proposed method. The results demonstrate the accuracy of the reconstructed signal depends on the sampling frequency, the blade vibration frequency, the blade vibration bandwidth, the probe static offset and the number of samples. In practice, both types of blade vibration signals can be particularly reconstructed by non-uniform BTT data acquired from only two probes.
A Multiobjective Sparse Feature Learning Model for Deep Neural Networks.
Gong, Maoguo; Liu, Jia; Li, Hao; Cai, Qing; Su, Linzhi
Hierarchical deep neural networks are currently popular learning models for imitating the hierarchical architecture of human brain. Single-layer feature extractors are the bricks to build deep networks. Sparse feature learning models are popular models that can learn useful representations. But most of those models need a user-defined constant to control the sparsity of representations. In this paper, we propose a multiobjective sparse feature learning model based on the autoencoder. The parameters of the model are learnt by optimizing two objectives, reconstruction error and the sparsity of hidden units simultaneously to find a reasonable compromise between them automatically. We design a multiobjective induced learning procedure for this model based on a multiobjective evolutionary algorithm. In the experiments, we demonstrate that the learning procedure is effective, and the proposed multiobjective model can learn useful sparse features.
Magnetic Resonance Super-resolution Imaging Measurement with Dictionary-optimized Sparse Learning
Li Jun-Bao
Full Text Available Magnetic Resonance Super-resolution Imaging Measurement (MRIM is an effective way of measuring materials. MRIM has wide applications in physics, chemistry, biology, geology, medical and material science, especially in medical diagnosis. It is feasible to improve the resolution of MR imaging through increasing radiation intensity, but the high radiation intensity and the longtime of magnetic field harm the human body. Thus, in the practical applications the resolution of hardware imaging reaches the limitation of resolution. Software-based super-resolution technology is effective to improve the resolution of image. This work proposes a framework of dictionary-optimized sparse learning based MR super-resolution method. The framework is to solve the problem of sample selection for dictionary learning of sparse reconstruction. The textural complexity-based image quality representation is proposed to choose the optimal samples for dictionary learning. Comprehensive experiments show that the dictionary-optimized sparse learning improves the performance of sparse representation.
Image reconstruction by domain-transform manifold learning
Zhu, Bo; Liu, Jeremiah Z.; Cauley, Stephen F.; Rosen, Bruce R.; Rosen, Matthew S.
Image reconstruction is essential for imaging applications across the physical and life sciences, including optical and radar systems, magnetic resonance imaging, X-ray computed tomography, positron emission tomography, ultrasound imaging and radio astronomy. During image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the exact inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain, the composition of which depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. Here we present a unified framework for image reconstruction—automated transform by manifold approximation (AUTOMAP)—which recasts image reconstruction as a data-driven supervised learning task that allows a mapping between the sensor and the image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for various magnetic resonance imaging acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate that manifold learning during training results in sparse representations of domain transforms along low-dimensional data manifolds, and observe superior immunity to noise and a reduction in reconstruction artefacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate that AUTOMAP and other learned reconstruction approaches will accelerate the development
Dense range images from sparse point clouds using multi-scale processing
Do, Q.L.; Ma, L.; With, de P.H.N.
Multi-modal data processing based on visual and depth/range images has become relevant in computer vision for 3D reconstruction applications such as city modeling, robot navigation etc. In this paper, we generate highaccuracy dense range images from sparse point clouds to facilitate such
Extra Facial Landmark Localization via Global Shape Reconstruction
Shuqiu Tan
Full Text Available Localizing facial landmarks is a popular topic in the field of face analysis. However, problems arose in practical applications such as handling pose variations and partial occlusions while maintaining moderate training model size and computational efficiency still challenges current solutions. In this paper, we present a global shape reconstruction method for locating extra facial landmarks comparing to facial landmarks used in the training phase. In the proposed method, the reduced configuration of facial landmarks is first decomposed into corresponding sparse coefficients. Then explicit face shape correlations are exploited to regress between sparse coefficients of different facial landmark configurations. Finally extra facial landmarks are reconstructed by combining the pretrained shape dictionary and the approximation of sparse coefficients. By applying the proposed method, both the training time and the model size of a class of methods which stack local evidences as an appearance descriptor can be scaled down with only a minor compromise in detection accuracy. Extensive experiments prove that the proposed method is feasible and is able to reconstruct extra facial landmarks even under very asymmetrical face poses.
High-Order Sparse Linear Predictors for Audio Processing
Giacobello, Daniele; van Waterschoot, Toon; Christensen, Mads Græsbøll
Linear prediction has generally failed to make a breakthrough in audio processing, as it has done in speech processing. This is mostly due to its poor modeling performance, since an audio signal is usually an ensemble of different sources. Nevertheless, linear prediction comes with a whole set...... of interesting features that make the idea of using it in audio processing not far fetched, e.g., the strong ability of modeling the spectral peaks that play a dominant role in perception. In this paper, we provide some preliminary conjectures and experiments on the use of high-order sparse linear predictors...... in audio processing. These predictors, successfully implemented in modeling the short-term and long-term redundancies present in speech signals, will be used to model tonal audio signals, both monophonic and polyphonic. We will show how the sparse predictors are able to model ef�ciently the different...
Some factors affecting time reversal signal reconstruction
Převorovský, Zdeněk; Kober, Jan
Ro�. 70, September (2015), s. 604-608 ISSN 1875-3892. [ICU International Congress on Ultrasonics 2015. Metz, 10.05.2015-15.05.2015] Institutional support: RVO:61388998 Keywords : nondestructive testing * time reversal signal processing * ultrasonic source reconstruction * acoustic emission * coda wave interferometry Subject RIV: BI - Acoustic s http://ac.els-cdn.com/S1875389215007762/1-s2.0-S1875389215007762-main.pdf?_tid=1513a4a2-9e5b-11e5-9693-00000aab0f27&acdnat=1449655153_455a4e32a1135236d0796c3f973ff58e
Behavior of greedy sparse representation algorithms on nested supports
Mailhé, Boris; Sturm, Bob L.; Plumbley, Mark
is not locally nested: there is a dictionary and supports Γ ⊃ Γ′ such that OMP can recover all signals with support Γ, but not all signals with support Γ′. We also show that the support recovery optimality of OMP is globally nested: if OMP can recover all s-sparse signals, then it can recover all s...
Two-dimensional sparse wavenumber recovery for guided wavefields
Sabeti, Soroosh; Harley, Joel B.
The multi-modal and dispersive behavior of guided waves is often characterized by their dispersion curves, which describe their frequency-wavenumber behavior. In prior work, compressive sensing based techniques, such as sparse wavenumber analysis (SWA), have been capable of recovering dispersion curves from limited data samples. A major limitation of SWA, however, is the assumption that the structure is isotropic. As a result, SWA fails when applied to composites and other anisotropic structures. There have been efforts to address this issue in the literature, but they either are not easily generalizable or do not sufficiently express the data. In this paper, we enhance the existing approaches by employing a two-dimensional wavenumber model to account for direction-dependent velocities in anisotropic media. We integrate this model with tools from compressive sensing to reconstruct a wavefield from incomplete data. Specifically, we create a modified two-dimensional orthogonal matching pursuit algorithm that takes an undersampled wavefield image, with specified unknown elements, and determines its sparse wavenumber characteristics. We then recover the entire wavefield from the sparse representations obtained with our small number of data samples.
Similarity regularized sparse group lasso for cup to disc ratio computation.
Cheng, Jun; Zhang, Zhuo; Tao, Dacheng; Wong, Damon Wing Kee; Liu, Jiang; Baskaran, Mani; Aung, Tin; Wong, Tien Yin
Automatic cup to disc ratio (CDR) computation from color fundus images has shown to be promising for glaucoma detection. Over the past decade, many algorithms have been proposed. In this paper, we first review the recent work in the area and then present a novel similarity-regularized sparse group lasso method for automated CDR estimation. The proposed method reconstructs the testing disc image based on a set of reference disc images by integrating the similarity between testing and the reference disc images with the sparse group lasso constraints. The reconstruction coefficients are then used to estimate the CDR of the testing image. The proposed method has been validated using 650 images with manually annotated CDRs. Experimental results show an average CDR error of 0.0616 and a correlation coefficient of 0.7, outperforming other methods. The areas under curve in the diagnostic test reach 0.843 and 0.837 when manual and automatically segmented discs are used respectively, better than other methods as well.
Speckle suppression via sparse representation for wide-field imaging through turbid media.
Jang, Hwanchol; Yoon, Changhyeong; Chung, Euiheon; Choi, Wonshik; Lee, Heung-No
Speckle suppression is one of the most important tasks in the image transmission through turbid media. Insufficient speckle suppression requires an additional procedure such as temporal ensemble averaging over multiple exposures. In this paper, we consider the image recovery process based on the so-called transmission matrix (TM) of turbid media for the image transmission through the media. We show that the speckle left unremoved in the TM-based image recovery can be suppressed effectively via sparse representation (SR). SR is a relatively new signal reconstruction framework which works well even for ill-conditioned problems. This is the first study to show the benefit of using the SR as compared to the phase conjugation (PC) a de facto standard method to date for TM-based imaging through turbid media including a live cell through tissue slice.
Speckle Reduction on Ultrasound Liver Images Based on a Sparse Representation over a Learned Dictionary
Mohamed Yaseen Jabarulla
Full Text Available Ultrasound images are corrupted with multiplicative noise known as speckle, which reduces the effectiveness of image processing and hampers interpretation. This paper proposes a multiplicative speckle suppression technique for ultrasound liver images, based on a new signal reconstruction model known as sparse representation (SR over dictionary learning. In the proposed technique, the non-uniform multiplicative signal is first converted into additive noise using an enhanced homomorphic filter. This is followed by pixel-based total variation (TV regularization and patch-based SR over a dictionary trained using K-singular value decomposition (KSVD. Finally, the split Bregman algorithm is used to solve the optimization problem and estimate the de-speckled image. The simulations performed on both synthetic and clinical ultrasound images for speckle reduction, the proposed technique achieved peak signal-to-noise ratios of 35.537 dB for the dictionary trained on noisy image patches and 35.033 dB for the dictionary trained using a set of reference ultrasound image patches. Further, the evaluation results show that the proposed method performs better than other state-of-the-art denoising algorithms in terms of both peak signal-to-noise ratio and subjective visual quality assessment.
Universal Regularizers For Robust Sparse Coding and Modeling
Ramirez, Ignacio; Sapiro, Guillermo
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding...
Consensus Convolutional Sparse Coding
Choudhury, Biswarup
Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision. In contrast to recent supervised methods, CSC allows for convolutional image representations to be learned that are equally useful for high-level vision tasks and low-level image reconstruction and can be applied to a wide range of tasks without problem-specific retraining. Due to their extreme memory requirements, however, existing CSC solvers have so far been limited to low-dimensional problems and datasets using a handful of low-resolution example images at a time. In this paper, we propose a new approach to solving CSC as a consensus optimization problem, which lifts these limitations. By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks. Moreover, the proposed method enables new applications in high-dimensional feature learning that has been intractable using existing CSC methods. This is demonstrated for a variety of reconstruction problems across diverse problem domains, including 3D multispectral demosaicing and 4D light field view synthesis.
Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision. In contrast to recent supervised methods, CSC allows for convolutional image representations to be learned that are equally useful for high-level vision tasks and low-level image reconstruction and can be applied to a wide range of tasks without problem-specific retraining. Due to their extreme memory requirements, however, existing CSC solvers have so far been limited to low-dimensional problems and datasets using a handful of low-resolution example images at a time. In this paper, we propose a new approach to solving CSC as a consensus optimization problem, which lifts these limitations. By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks. Moreover, the proposed method enables new applications in high dimensional feature learning that has been intractable using existing CSC methods. This is demonstrated for a variety of reconstruction problems across diverse problem domains, including 3D multispectral demosaickingand 4D light field view synthesis.
Choudhury, Biswarup; Swanson, Robin; Heide, Felix; Wetzstein, Gordon; Heidrich, Wolfgang
Non-Cartesian MRI scan time reduction through sparse sampling
Wajer, F.T.A.W.
Non-Cartesian MRI Scan-Time Reduction through Sparse Sampling Magnetic resonance imaging (MRI) signals are measured in the Fourier domain, also called k-space. Samples of the MRI signal can not be taken at will, but lie along k-space trajectories determined by the magnetic field gradients. MRI
Compressed sensing for energy-efficient wireless telemonitoring of noninvasive fetal ECG via block sparse Bayesian learning.
Zhang, Zhilin; Jung, Tzyy-Ping; Makeig, Scott; Rao, Bhaskar D
Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as nonsparsity and strong noise contamination, current CS algorithms generally fail in this application. This paper proposes to use the block sparse Bayesian learning framework to compress/reconstruct nonsparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows that the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.
Full Text Available Multiple-input multiple-output (MIMO radar takes the advantages of high degrees of freedom for beam pattern design and waveform optimization, because each antenna in centralized MIMO radar system can transmit different signal waveforms. When continuous band is divided into several pieces, sparse frequency radar waveforms play an important role due to the special pattern of the sparse spectrum. In this paper, we start from the covariance matrix of the transmitted waveform and extend the concept of sparse frequency design to the study of MIMO radar beam pattern. With this idea in mind, we first solve the problem of semidefinite constraint by optimization tools and get the desired covariance matrix of the ideal beam pattern. Then, we use the acquired covariance matrix and generalize the objective function by adding the constraint of both constant modulus of the signals and corresponding spectrum. Finally, we solve the objective function by the cyclic algorithm and obtain the sparse frequency MIMO radar waveforms with desired beam pattern. The simulation results verify the effectiveness of this method.
Wavelets for Sparse Representation of Music
Endelt, Line Ørtoft; Harbo, Anders La-Cour
We are interested in obtaining a sparse representation of music signals by means of a discrete wavelet transform (DWT). That means we want the energy in the representation to be concentrated in few DWT coefficients. It is well-known that the decay of the DWT coefficients is strongly related...... to the number of vanishing moments of the mother wavelet, and to the smoothness of the signal. In this paper we present the result of applying two classical families of wavelets to a series of musical signals. The purpose is to determine a general relation between the number of vanishing moments of the wavelet...
A FPC-ROOT Algorithm for 2D-DOA Estimation in Sparse Array
Wenhao Zeng
Full Text Available To improve the performance of two-dimensional direction-of-arrival (2D DOA estimation in sparse array, this paper presents a Fixed Point Continuation Polynomial Roots (FPC-ROOT algorithm. Firstly, a signal model for DOA estimation is established based on matrix completion and it can be proved that the proposed model meets Null Space Property (NSP. Secondly, left and right singular vectors of received signals matrix are achieved using the matrix completion algorithm. Finally, 2D DOA estimation can be acquired through solving the polynomial roots. The proposed algorithm can achieve high accuracy of 2D DOA estimation in sparse array, without solving autocorrelation matrix of received signals and scanning of two-dimensional spectral peak. Besides, it decreases the number of antennas and lowers computational complexity and meanwhile avoids the angle ambiguity problem. Computer simulations demonstrate that the proposed FPC-ROOT algorithm can obtain the 2D DOA estimation precisely in sparse array.
Intensity-based bayesian framework for image reconstruction from sparse projection data
Rashed, E.A.; Kudo, Hiroyuki
This paper presents a Bayesian framework for iterative image reconstruction from projection data measured over a limited number of views. The classical Nyquist sampling rule yields the minimum number of projection views required for accurate reconstruction. However, challenges exist in many medical and industrial imaging applications in which the projection data is undersampled. Classical analytical reconstruction methods such as filtered backprojection (FBP) are not a good choice for use in such cases because the data undersampling in the angular range introduces aliasing and streak artifacts that degrade lesion detectability. In this paper, we propose a Bayesian framework for maximum likelihood-expectation maximization (ML-EM)-based iterative reconstruction methods that incorporates a priori knowledge obtained from expected intensity information. The proposed framework is based on the fact that, in tomographic imaging, it is often possible to expect a set of intensity values of the reconstructed object with relatively high accuracy. The image reconstruction cost function is modified to include the l 1 norm distance to the a priori known information. The proposed method has the potential to regularize the solution to reduce artifacts without missing lesions that cannot be expected from the a priori information. Numerical studies showed a significant improvement in image quality and lesion detectability under the condition of highly undersampled projection data. (author)
Abnormal Event Detection Using Local Sparse Representation
Ren, Huamin; Moeslund, Thomas B.
We propose to detect abnormal events via a sparse subspace clustering algorithm. Unlike most existing approaches, which search for optimized normal bases and detect abnormality based on least square error or reconstruction error from the learned normal patterns, we propose an abnormality measurem...... is found that satisfies: the distance between its local space and the normal space is large. We evaluate our method on two public benchmark datasets: UCSD and Subway Entrance datasets. The comparison to the state-of-the-art methods validate our method's effectiveness....
P-Finder: Reconstruction of Signaling Networks from Protein-Protein Interactions and GO Annotations.
Young-Rae Cho; Yanan Xin; Speegle, Greg
Because most complex genetic diseases are caused by defects of cell signaling, illuminating a signaling cascade is essential for understanding their mechanisms. We present three novel computational algorithms to reconstruct signaling networks between a starting protein and an ending protein using genome-wide protein-protein interaction (PPI) networks and gene ontology (GO) annotation data. A signaling network is represented as a directed acyclic graph in a merged form of multiple linear pathways. An advanced semantic similarity metric is applied for weighting PPIs as the preprocessing of all three methods. The first algorithm repeatedly extends the list of nodes based on path frequency towards an ending protein. The second algorithm repeatedly appends edges based on the occurrence of network motifs which indicate the link patterns more frequently appearing in a PPI network than in a random graph. The last algorithm uses the information propagation technique which iteratively updates edge orientations based on the path strength and merges the selected directed edges. Our experimental results demonstrate that the proposed algorithms achieve higher accuracy than previous methods when they are tested on well-studied pathways of S. cerevisiae. Furthermore, we introduce an interactive web application tool, called P-Finder, to visualize reconstructed signaling networks.
Analysing 21cm signal with artificial neural network
Shimabukuro, Hayato; a Semelin, Benoit
The 21cm signal at epoch of reionization (EoR) should be observed within next decade. We expect that cosmic 21cm signal at the EoR provides us both cosmological and astrophysical information. In order to extract fruitful information from observation data, we need to develop inversion method. For such a method, we introduce artificial neural network (ANN) which is one of the machine learning techniques. We apply the ANN to inversion problem to constrain astrophysical parameters from 21cm power spectrum. We train the architecture of the neural network with 70 training datasets and apply it to 54 test datasets with different value of parameters. We find that the quality of the parameter reconstruction depends on the sensitivity of the power spectrum to the different parameter sets at a given redshift and also find that the accuracy of reconstruction is improved by increasing the number of given redshifts. We conclude that the ANN is viable inversion method whose main strength is that they require a sparse extrapolation of the parameter space and thus should be usable with full simulation.
Accurate reconstruction in digital holographic microscopy using Fresnel dual-tree complex wavelet transform
Zhang, Xiaolei; Zhang, Xiangchao; Yuan, He; Zhang, Hao; Xu, Min
Digital holography is a promising measurement method in the fields of bio-medicine and micro-electronics. But the captured images of digital holography are severely polluted by the speckle noise because of optical scattering and diffraction. Via analyzing the properties of Fresnel diffraction and the topographies of micro-structures, a novel reconstruction method based on the dual-tree complex wavelet transform (DT-CWT) is proposed. This algorithm is shiftinvariant and capable of obtaining sparse representations for the diffracted signals of salient features, thus it is well suited for multiresolution processing of the interferometric holograms of directional morphologies. An explicit representation of orthogonal Fresnel DT-CWT bases and a specific filtering method are developed. This method can effectively remove the speckle noise without destroying the salient features. Finally, the proposed reconstruction method is compared with the conventional Fresnel diffraction integration and Fresnel wavelet transform with compressive sensing methods to validate its remarkable superiority on the aspects of topography reconstruction and speckle removal.
Investigation on magnetoacoustic signal generation with magnetic induction and its application to electrical conductivity reconstruction
Ma Qingyu; He Bin
A theoretical study on the magnetoacoustic signal generation with magnetic induction and its applications to electrical conductivity reconstruction is conducted. An object with a concentric cylindrical geometry is located in a static magnetic field and a pulsed magnetic field. Driven by Lorentz force generated by the static magnetic field, the magnetically induced eddy current produces acoustic vibration and the propagated sound wave is received by a transducer around the object to reconstruct the corresponding electrical conductivity distribution of the object. A theory on the magnetoacoustic waveform generation for a circular symmetric model is provided as a forward problem. The explicit formulae and quantitative algorithm for the electrical conductivity reconstruction are then presented as an inverse problem. Computer simulations were conducted to test the proposed theory and assess the performance of the inverse algorithms for a multi-layer cylindrical model. The present simulation results confirm the validity of the proposed theory and suggest the feasibility of reconstructing electrical conductivity distribution based on the proposed theory on the magnetoacoustic signal generation with magnetic induction
Compressive Sensing of Roller Bearing Faults via Harmonic Detection from Under-Sampled Vibration Signals.
Tang, Gang; Hou, Wei; Wang, Huaqing; Luo, Ganggang; Ma, Jianwei
The Shannon sampling principle requires substantial amounts of data to ensure the accuracy of on-line monitoring of roller bearing fault signals. Challenges are often encountered as a result of the cumbersome data monitoring, thus a novel method focused on compressed vibration signals for detecting roller bearing faults is developed in this study. Considering that harmonics often represent the fault characteristic frequencies in vibration signals, a compressive sensing frame of characteristic harmonics is proposed to detect bearing faults. A compressed vibration signal is first acquired from a sensing matrix with information preserved through a well-designed sampling strategy. A reconstruction process of the under-sampled vibration signal is then pursued as attempts are conducted to detect the characteristic harmonics from sparse measurements through a compressive matching pursuit strategy. In the proposed method bearing fault features depend on the existence of characteristic harmonics, as typically detected directly from compressed data far before reconstruction completion. The process of sampling and detection may then be performed simultaneously without complete recovery of the under-sampled signals. The effectiveness of the proposed method is validated by simulations and experiments.
Spectrum recovery method based on sparse representation for segmented multi-Gaussian model
Teng, Yidan; Zhang, Ye; Ti, Chunli; Su, Nan
Hyperspectral images can realize crackajack features discriminability for supplying diagnostic characteristics with high spectral resolution. However, various degradations may generate negative influence on the spectral information, including water absorption, bands-continuous noise. On the other hand, the huge data volume and strong redundancy among spectrums produced intense demand on compressing HSIs in spectral dimension, which also leads to the loss of spectral information. The reconstruction of spectral diagnostic characteristics has irreplaceable significance for the subsequent application of HSIs. This paper introduces a spectrum restoration method for HSIs making use of segmented multi-Gaussian model (SMGM) and sparse representation. A SMGM is established to indicating the unsymmetrical spectral absorption and reflection characteristics, meanwhile, its rationality and sparse property are discussed. With the application of compressed sensing (CS) theory, we implement sparse representation to the SMGM. Then, the degraded and compressed HSIs can be reconstructed utilizing the uninjured or key bands. Finally, we take low rank matrix recovery (LRMR) algorithm for post processing to restore the spatial details. The proposed method was tested on the spectral data captured on the ground with artificial water absorption condition and an AVIRIS-HSI data set. The experimental results in terms of qualitative and quantitative assessments demonstrate that the effectiveness on recovering the spectral information from both degradations and loss compression. The spectral diagnostic characteristics and the spatial geometry feature are well preserved.
Sparse coding reveals greater functional connectivity in female brains during naturalistic emotional experience.
Yudan Ren
Full Text Available Functional neuroimaging is widely used to examine changes in brain function associated with age, gender or neuropsychiatric conditions. FMRI (functional magnetic resonance imaging studies employ either laboratory-designed tasks that engage the brain with abstracted and repeated stimuli, or resting state paradigms with little behavioral constraint. Recently, novel neuroimaging paradigms using naturalistic stimuli are gaining increasing attraction, as they offer an ecologically-valid condition to approximate brain function in real life. Wider application of naturalistic paradigms in exploring individual differences in brain function, however, awaits further advances in statistical methods for modeling dynamic and complex dataset. Here, we developed a novel data-driven strategy that employs group sparse representation to assess gender differences in brain responses during naturalistic emotional experience. Comparing to independent component analysis (ICA, sparse coding algorithm considers the intrinsic sparsity of neural coding and thus could be more suitable in modeling dynamic whole-brain fMRI signals. An online dictionary learning and sparse coding algorithm was applied to the aggregated fMRI signals from both groups, which was subsequently factorized into a common time series signal dictionary matrix and the associated weight coefficient matrix. Our results demonstrate that group sparse representation can effectively identify gender differences in functional brain network during natural viewing, with improved sensitivity and reliability over ICA-based method. Group sparse representation hence offers a superior data-driven strategy for examining brain function during naturalistic conditions, with great potential for clinical application in neuropsychiatric disorders.
Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Badiu, Mihai Alin
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued m......In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex...... error, and robustness in low and medium signal-to-noise ratio regimes....
Advances in thermographic signal reconstruction
Shepard, Steven M.; Frendberg Beemer, Maria
Since its introduction in 2001, the Thermographic Signal Reconstruction (TSR) method has emerged as one of the most widely used methods for enhancement and analysis of thermographic sequences, with applications extending beyond industrial NDT into biomedical research, art restoration and botany. The basic TSR process, in which a noise reduced replica of each pixel time history is created, yields improvement over unprocessed image data that is sufficient for many applications. However, examination of the resulting logarithmic time derivatives of each TSR pixel replica provides significant insight into the physical mechanisms underlying the active thermography process. The deterministic and invariant properties of the derivatives have enabled the successful implementation of automated defect recognition and measurement systems. Unlike most approaches to analysis of thermography data, TSR does not depend on flawbackground contrast, so that it can also be applied to characterization and measurement of thermal properties of flaw-free samples. We present a summary of recent advances in TSR, a review of the underlying theory and examples of its implementation.
Reconstruction and measurement of cosmogenic signals in the neutrino experiment Borexino
Meindl, Johannes Quirin
Underground laboratories around the globe provide low-count rate experiments with the necessary shielding against the large flux of cosmic muons present at the Earth's surface. Depending on the depth of the underground site, the muon flux is reduced by up to eight orders of magnitude. Hower, the residual muons, and the neutrons and radioisotopes they produce in nuclear spallation processes, still pose a significant background for many of these experiments. This thesis focusses on cosmogenic background signals in the neutrino experiment Borexino, which is located at the Laboratori Nazionali del Gran Sasso underground site at a depth of 3800 meters of water equivalent. The work encompasses the identification, spatial reconstruction, and measurement of rates and production yields of these cosmogenic events. For the efficient tagging of long-lived cosmogenic radioisotopes of lifetimes in the order of seconds and longer, the spatial reconstruction of the parent muon is essential. Based on the characteristic light emission profile of muons crossing the inner detector of Borexino, a new muon track reconstruction algorithm was developed. Furthermore, to increase the performance of the existing muon track reconstruction of Borexino's outer detector, a routine was programmed to automatically calibrate the photomultiplier tubes in timing and charge response. Muons entering the experiment can cause fast secondary signals from decays and captures of stopped muons, and the captures of muon-induced neutrons. To identify these events in the high noise environment after the muon, dedicated search algorithms were developed. Based on the detected signals, these fast muon-correlated events are studied. The fraction and lifetime of stopped muons are found to be in agreement with expectations. The production yield of cosmogenic neutrons is measured to (3.10±0.07 stat ±0.08 syst ) . 10 -4 n/(μ . (g/cm 2 )). The corresponding capture time in the Borexino scintillator pseudocumene is
Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding
Ying Chen
Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.
Macromolecular 3D SEM reconstruction strategies: Signal to noise ratio and resolution
Woodward, J.D.; Wepf, R.A.
Three-dimensional scanning electron microscopy generates quantitative volumetric structural data from SEM images of macromolecules. This technique provides a quick and easy way to define the quaternary structure and handedness of protein complexes. Here, we apply a variety of preparation and imaging methods to filamentous actin in order to explore the relationship between resolution, signal-to-noise ratio, structural preservation and dataset size. This information can be used to define successful imaging strategies for different applications. - Highlights: • F-actin SEM datasets were collected using 8 different preparation/ imaging techniques. • Datasets were reconstructed by back projection and compared/analyzed • 3DSEM actin reconstructions can be produced with <100 views of the asymmetric unit. • Negatively stained macromolecules can be reconstructed by 3DSEM to ∼3 nm resolution
A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system
Liu, Wenyang [Department of Bioengineering, University of California, Los Angeles, Los Angeles, California 90095 (United States); Cheung, Yam [Department of Radiation Oncology, University of Texas Southwestern, Dallas, Texas 75390 (United States); Sawant, Amit [Department of Radiation Oncology, University of Texas Southwestern, Dallas, Texas, 75390 and Department of Radiation Oncology, University of Maryland, College Park, Maryland 20742 (United States); Ruan, Dan, E-mail: druan@mednet.ucla.edu [Department of Bioengineering, University of California, Los Angeles, Los Angeles, California 90095 and Department of Radiation Oncology, University of California, Los Angeles, Los Angeles, California 90095 (United States)
Purpose: To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. Methods: The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. Results: On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced
A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system.
Liu, Wenyang; Cheung, Yam; Sawant, Amit; Ruan, Dan
To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. The authors have
Semi-supervised sparse coding
Wang, Jim Jing-Yan; Gao, Xin
Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.
An Improved Information Hiding Method Based on Sparse Representation
Minghai Yao
Full Text Available A novel biometric authentication information hiding method based on the sparse representation is proposed for enhancing the security of biometric information transmitted in the network. In order to make good use of abundant information of the cover image, the sparse representation method is adopted to exploit the correlation between the cover and biometric images. Thus, the biometric image is divided into two parts. The first part is the reconstructed image, and the other part is the residual image. The biometric authentication image cannot be restored by any one part. The residual image and sparse representation coefficients are embedded into the cover image. Then, for the sake of causing much less attention of attackers, the visual attention mechanism is employed to select embedding location and embedding sequence of secret information. Finally, the reversible watermarking algorithm based on histogram is utilized for embedding the secret information. For verifying the validity of the algorithm, the PolyU multispectral palmprint and the CASIA iris databases are used as biometric information. The experimental results show that the proposed method exhibits good security, invisibility, and high capacity.
Segmentation of MR images via discriminative dictionary learning and sparse coding: Application to hippocampus labeling
Tong, Tong; Wolz, Robin; Coupe, Pierrick; Hajnal, Joseph V.; Rueckert, Daniel
International audience; We propose a novel method for the automatic segmentation of brain MRI images by using discriminative dictionary learning and sparse coding techniques. In the proposed method, dictionaries and classifiers are learned simultaneously from a set of brain atlases, which can then be used for the reconstruction and segmentation of an unseen target image. The proposed segmentation strategy is based on image reconstruction, which is in contrast to most existing atlas-based labe...
Task-based optimization of image reconstruction in breast CT
Sanchez, Adrian A.; Sidky, Emil Y.; Pan, Xiaochuan
We demonstrate a task-based assessment of image quality in dedicated breast CT in order to optimize the number of projection views acquired. The methodology we employ is based on the Hotelling Observer (HO) and its associated metrics. We consider two tasks: the Rayleigh task of discerning between two resolvable objects and a single larger object, and the signal detection task of classifying an image as belonging to either a signalpresent or signal-absent hypothesis. HO SNR values are computed for 50, 100, 200, 500, and 1000 projection view images, with the total imaging radiation dose held constant. We use the conventional fan-beam FBP algorithm and investigate the effect of varying the width of a Hanning window used in the reconstruction, since this affects both the noise properties of the image and the under-sampling artifacts which can arise in the case of sparse-view acquisitions. Our results demonstrate that fewer projection views should be used in order to increase HO performance, which in this case constitutes an upper-bound on human observer performance. However, the impact on HO SNR of using fewer projection views, each with a higher dose, is not as significant as the impact of employing regularization in the FBP reconstruction through a Hanning filter.
Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm
An efficient electromagnetic inversion scheme for imaging sparse 3-D domains is proposed. The scheme achieves its efficiency and accuracy by integrating two concepts. First, the nonlinear optimization problem is constrained using L₀ or L�-norm of the solution as the penalty term to alleviate the ill-posedness of the inverse problem. The resulting Tikhonov minimization problem is solved using nonlinear Landweber iterations (NLW). Second, the efficiency of the NLW is significantly increased using a steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without sacrificing the convergence of the algorithm. Numerical results demonstrate the efficiency and accuracy of the proposed imaging scheme in reconstructing sparse 3-D dielectric profiles.
Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA for L p -Regularization Using the Multiple Sub-Dictionary Representation
Yunyi Li
Full Text Available Both L 1 / 2 and L 2 / 3 are two typical non-convex regularizations of L p ( 0 < p < 1 , which can be employed to obtain a sparser solution than the L 1 regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in L 1 regularization for sparse signal recovery, which combines the iterative reweighted algorithms. To further exploit the sparse structure of signal and image, this paper adopts multiple dictionary sparse transform strategies for the two typical cases p ∈ { 1 / 2 ,  2 / 3 } based on an iterative L p thresholding algorithm and then proposes a sparse adaptive iterative-weighted L p thresholding algorithm (SAITA. Moreover, a simple yet effective regularization parameter is proposed to weight each sub-dictionary-based L p regularizer. Simulation results have shown that the proposed SAITA not only performs better than the corresponding L 1 algorithms but can also obtain a better recovery performance and achieve faster convergence than the conventional single-dictionary sparse transform-based L p case. Moreover, we conduct some applications about sparse image recovery and obtain good results by comparison with relative work.
Sparse-view proton computed tomography using modulated proton beams
Lee, Jiseoc; Kim, Changhwan; Cho, Seungryong, E-mail: scho@kaist.ac.kr [Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701 (Korea, Republic of); Min, Byungjun [Department of Radiation Oncology, Kangbuk Samsung Hospital, 110–746 (Korea, Republic of); Kwak, Jungwon [Department of Radiation Oncology, Asan Medical Center, 138–736 (Korea, Republic of); Park, Seyjoon; Lee, Se Byeong [Proton Therapy Center, National Cancer Center, 410–769 (Korea, Republic of); Park, Sungyong [Proton Therapy Center, McLaren Cancer Institute, Flint, Michigan 48532 (United States)
Purpose: Proton imaging that uses a modulated proton beam and an intensity detector allows a relatively fast image acquisition compared to the imaging approach based on a trajectory tracking detector. In addition, it requires a relatively simple implementation in a conventional proton therapy equipment. The model of geometric straight ray assumed in conventional computed tomography (CT) image reconstruction is however challenged by multiple-Coulomb scattering and energy straggling in the proton imaging. Radiation dose to the patient is another important issue that has to be taken care of for practical applications. In this work, the authors have investigated iterative image reconstructions after a deconvolution of the sparsely view-sampled data to address these issues in proton CT. Methods: Proton projection images were acquired using the modulated proton beams and the EBT2 film as an intensity detector. Four electron-density cylinders representing normal soft tissues and bone were used as imaged object and scanned at 40 views that are equally separated over 360°. Digitized film images were converted to water-equivalent thickness by use of an empirically derived conversion curve. For improving the image quality, a deconvolution-based image deblurring with an empirically acquired point spread function was employed. They have implemented iterative image reconstruction algorithms such as adaptive steepest descent-projection onto convex sets (ASD-POCS), superiorization method–projection onto convex sets (SM-POCS), superiorization method–expectation maximization (SM-EM), and expectation maximization-total variation minimization (EM-TV). Performance of the four image reconstruction algorithms was analyzed and compared quantitatively via contrast-to-noise ratio (CNR) and root-mean-square-error (RMSE). Results: Objects of higher electron density have been reconstructed more accurately than those of lower density objects. The bone, for example, has been reconstructed
Detecting Activation in fMRI Data: An Approach Based on Sparse Representation of BOLD Signal
Blanca Guillen
Full Text Available This paper proposes a simple yet effective approach for detecting activated voxels in fMRI data by exploiting the inherent sparsity property of the BOLD signal in temporal and spatial domains. In the time domain, the approach combines the General Linear Model (GLM with a Least Absolute Deviation (LAD based regression method regularized by the pseudonorm l0 to promote sparsity in the parameter vector of the model. In the spatial domain, detection of activated regions is based on thresholding the spatial map of estimated parameters associated with a particular stimulus. The threshold is calculated by exploiting the sparseness of the BOLD signal in the spatial domain assuming a Laplacian distribution model. The proposed approach is validated using synthetic and real fMRI data. For synthetic data, results show that the proposed approach is able to detect most activated voxels without any false activation. For real data, the method is evaluated through comparison with the SPM software. Results indicate that this approach can effectively find activated regions that are similar to those found by SPM, but using a much simpler approach. This study may lead to the development of robust spatial approaches to further simplifying the complexity of classical schemes.
Non-Local Sparse Image Inpainting for Document Bleed-Through Removal
Muhammad Hanif
Full Text Available Bleed-through is a frequent, pervasive degradation in ancient manuscripts, which is caused by ink seeped from the opposite side of the sheet. Bleed-through, appearing as an extra interfering text, hinders document readability and makes it difficult to decipher the information contents. Digital image restoration techniques have been successfully employed to remove or significantly reduce this distortion. This paper proposes a two-step restoration method for documents affected by bleed-through, exploiting information from the recto and verso images. First, the bleed-through pixels are identified, based on a non-stationary, linear model of the two texts overlapped in the recto-verso pair. In the second step, a dictionary learning-based sparse image inpainting technique, with non-local patch grouping, is used to reconstruct the bleed-through-contaminated image information. An overcomplete sparse dictionary is learned from the bleed-through-free image patches, which is then used to estimate a befitting fill-in for the identified bleed-through pixels. The non-local patch similarity is employed in the sparse reconstruction of each patch, to enforce the local similarity. Thanks to the intrinsic image sparsity and non-local patch similarity, the natural texture of the background is well reproduced in the bleed-through areas, and even a possible overestimation of the bleed through pixels is effectively corrected, so that the original appearance of the document is preserved. We evaluate the performance of the proposed method on the images of a popular database of ancient documents, and the results validate the performance of the proposed method compared to the state of the art.
Sparse Representation Based Binary Hypothesis Model for Hyperspectral Image Classification
Yidong Tang
Full Text Available The sparse representation based classifier (SRC and its kernel version (KSRC have been employed for hyperspectral image (HSI classification. However, the state-of-the-art SRC often aims at extended surface objects with linear mixture in smooth scene and assumes that the number of classes is given. Considering the small target with complex background, a sparse representation based binary hypothesis (SRBBH model is established in this paper. In this model, a query pixel is represented in two ways, which are, respectively, by background dictionary and by union dictionary. The background dictionary is composed of samples selected from the local dual concentric window centered at the query pixel. Thus, for each pixel the classification issue becomes an adaptive multiclass classification problem, where only the number of desired classes is required. Furthermore, the kernel method is employed to improve the interclass separability. In kernel space, the coding vector is obtained by using kernel-based orthogonal matching pursuit (KOMP algorithm. Then the query pixel can be labeled by the characteristics of the coding vectors. Instead of directly using the reconstruction residuals, the different impacts the background dictionary and union dictionary have on reconstruction are used for validation and classification. It enhances the discrimination and hence improves the performance.
Underground laboratories around the globe provide low-count rate experiments with the necessary shielding against the large flux of cosmic muons present at the Earth's surface. Depending on the depth of the underground site, the muon flux is reduced by up to eight orders of magnitude. Hower, the residual muons, and the neutrons and radioisotopes they produce in nuclear spallation processes, still pose a significant background for many of these experiments. This thesis focusses on cosmogenic background signals in the neutrino experiment Borexino, which is located at the Laboratori Nazionali del Gran Sasso underground site at a depth of 3800 meters of water equivalent. The work encompasses the identification, spatial reconstruction, and measurement of rates and production yields of these cosmogenic events. For the efficient tagging of long-lived cosmogenic radioisotopes of lifetimes in the order of seconds and longer, the spatial reconstruction of the parent muon is essential. Based on the characteristic light emission profile of muons crossing the inner detector of Borexino, a new muon track reconstruction algorithm was developed. Furthermore, to increase the performance of the existing muon track reconstruction of Borexino's outer detector, a routine was programmed to automatically calibrate the photomultiplier tubes in timing and charge response. Muons entering the experiment can cause fast secondary signals from decays and captures of stopped muons, and the captures of muon-induced neutrons. To identify these events in the high noise environment after the muon, dedicated search algorithms were developed. Based on the detected signals, these fast muon-correlated events are studied. The fraction and lifetime of stopped muons are found to be in agreement with expectations. The production yield of cosmogenic neutrons is measured to (3.10{+-}0.07{sub stat}{+-}0.08{sub syst}) . 10{sup -4} n/({mu} . (g/cm{sup 2})). The corresponding capture time in the
Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.
Rybicki, F J; Hrovat, M I; Patz, S
We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.
Low-dose X-ray CT reconstruction via dictionary learning.
Xu, Qiong; Yu, Hengyong; Mou, Xuanqin; Zhang, Lei; Hsieh, Jiang; Wang, Ge
Although diagnostic medical imaging provides enormous benefits in the early detection and accuracy diagnosis of various diseases, there are growing concerns on the potential side effect of radiation induced genetic, cancerous and other diseases. How to reduce radiation dose while maintaining the diagnostic performance is a major challenge in the computed tomography (CT) field. Inspired by the compressive sensing theory, the sparse constraint in terms of total variation (TV) minimization has already led to promising results for low-dose CT reconstruction. Compared to the discrete gradient transform used in the TV method, dictionary learning is proven to be an effective way for sparse representation. On the other hand, it is important to consider the statistical property of projection data in the low-dose CT case. Recently, we have developed a dictionary learning based approach for low-dose X-ray CT. In this paper, we present this method in detail and evaluate it in experiments. In our method, the sparse constraint in terms of a redundant dictionary is incorporated into an objective function in a statistical iterative reconstruction framework. The dictionary can be either predetermined before an image reconstruction task or adaptively defined during the reconstruction process. An alternating minimization scheme is developed to minimize the objective function. Our approach is evaluated with low-dose X-ray projections collected in animal and human CT studies, and the improvement associated with dictionary learning is quantified relative to filtered backprojection and TV-based reconstructions. The results show that the proposed approach might produce better images with lower noise and more detailed structural features in our selected cases. However, there is no proof that this is true for all kinds of structures.
Reconstruction and signal propagation analysis of the Syk signaling network in breast cancer cells.
Aurélien Naldi
Full Text Available The ability to build in-depth cell signaling networks from vast experimental data is a key objective of computational biology. The spleen tyrosine kinase (Syk protein, a well-characterized key player in immune cell signaling, was surprisingly first shown by our group to exhibit an onco-suppressive function in mammary epithelial cells and corroborated by many other studies, but the molecular mechanisms of this function remain largely unsolved. Based on existing proteomic data, we report here the generation of an interaction-based network of signaling pathways controlled by Syk in breast cancer cells. Pathway enrichment of the Syk targets previously identified by quantitative phospho-proteomics indicated that Syk is engaged in cell adhesion, motility, growth and death. Using the components and interactions of these pathways, we bootstrapped the reconstruction of a comprehensive network covering Syk signaling in breast cancer cells. To generate in silico hypotheses on Syk signaling propagation, we developed a method allowing to rank paths between Syk and its targets. We first annotated the network according to experimental datasets. We then combined shortest path computation with random walk processes to estimate the importance of individual interactions and selected biologically relevant pathways in the network. Molecular and cell biology experiments allowed to distinguish candidate mechanisms that underlie the impact of Syk on the regulation of cortactin and ezrin, both involved in actin-mediated cell adhesion and motility. The Syk network was further completed with the results of our biological validation experiments. The resulting Syk signaling sub-networks can be explored via an online visualization platform.
Optimization of image quality and acquisition time for lab-based X-ray microtomography using an iterative reconstruction algorithm
Lin, Qingyang; Andrew, Matthew; Thompson, William; Blunt, Martin J.; Bijeljic, Branko
Non-invasive laboratory-based X-ray microtomography has been widely applied in many industrial and research disciplines. However, the main barrier to the use of laboratory systems compared to a synchrotron beamline is its much longer image acquisition time (hours per scan compared to seconds to minutes at a synchrotron), which results in limited application for dynamic in situ processes. Therefore, the majority of existing laboratory X-ray microtomography is limited to static imaging; relatively fast imaging (tens of minutes per scan) can only be achieved by sacrificing imaging quality, e.g. reducing exposure time or number of projections. To alleviate this barrier, we introduce an optimized implementation of a well-known iterative reconstruction algorithm that allows users to reconstruct tomographic images with reasonable image quality, but requires lower X-ray signal counts and fewer projections than conventional methods. Quantitative analysis and comparison between the iterative and the conventional filtered back-projection reconstruction algorithm was performed using a sandstone rock sample with and without liquid phases in the pore space. Overall, by implementing the iterative reconstruction algorithm, the required image acquisition time for samples such as this, with sparse object structure, can be reduced by a factor of up to 4 without measurable loss of sharpness or signal to noise ratio.
Mapping visual stimuli to perceptual decisions via sparse decoding of mesoscopic neural activity.
Sajda, Paul
In this talk I will describe our work investigating sparse decoding of neural activity, given a realistic mapping of the visual scene to neuronal spike trains generated by a model of primary visual cortex (V1). We use a linear decoder which imposes sparsity via an L1 norm. The decoder can be viewed as a decoding neuron (linear summation followed by a sigmoidal nonlinearity) in which there are relatively few non-zero synaptic weights. We find: (1) the best decoding performance is for a representation that is sparse in both space and time, (2) decoding of a temporal code results in better performance than a rate code and is also a better fit to the psychophysical data, (3) the number of neurons required for decoding increases monotonically as signal-to-noise in the stimulus decreases, with as little as 1% of the neurons required for decoding at the highest signal-to-noise levels, and (4) sparse decoding results in a more accurate decoding of the stimulus and is a better fit to psychophysical performance than a distributed decoding, for example one imposed by an L2 norm. We conclude that sparse coding is well-justified from a decoding perspective in that it results in a minimum number of neurons and maximum accuracy when sparse representations can be decoded from the neural dynamics.
Single-Trial Evoked Potential Estimating Based on Sparse Coding under Impulsive Noise Environment
Nannan Yu
Full Text Available Estimating single-trial evoked potentials (EPs corrupted by the spontaneous electroencephalogram (EEG can be regarded as signal denoising problem. Sparse coding has significant success in signal denoising and EPs have been proven to have strong sparsity over an appropriate dictionary. In sparse coding, the noise generally is considered to be a Gaussian random process. However, some studies have shown that the background noise in EPs may present an impulsive characteristic which is far from Gaussian but suitable to be modeled by the α-stable distribution 1sparse coding will degrade or even fail. In view of this, we present a new sparse coding algorithm using p-norm optimization in single-trial EPs estimating. The algorithm can track the underlying EPs corrupted by α-stable distribution noise, trial-by-trial, without the need to estimate the α value. Simulations and experiments on human visual evoked potentials and event-related potentials are carried out to examine the performance of the proposed approach. Experimental results show that the proposed method is effective in estimating single-trial EPs under impulsive noise environment.
3D Reconstruction of human bones based on dictionary learning.
Zhang, Binkai; Wang, Xiang; Liang, Xiao; Zheng, Jinjin
An effective method for reconstructing a 3D model of human bones from computed tomography (CT) image data based on dictionary learning is proposed. In this study, the dictionary comprises the vertices of triangular meshes, and the sparse coefficient matrix indicates the connectivity information. For better reconstruction performance, we proposed a balance coefficient between the approximation and regularisation terms and a method for optimisation. Moreover, we applied a local updating strategy and a mesh-optimisation method to update the dictionary and the sparse matrix, respectively. The two updating steps are iterated alternately until the objective function converges. Thus, a reconstructed mesh could be obtained with high accuracy and regularisation. The experimental results show that the proposed method has the potential to obtain high precision and high-quality triangular meshes for rapid prototyping, medical diagnosis, and tissue engineering. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.
Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency.
Zhang, Ying-Ying; Yang, Cai; Zhang, Ping
In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.
A Sparse Bayesian Learning Algorithm With Dictionary Parameter Estimation
Hansen, Thomas Lundgaard; Badiu, Mihai Alin; Fleury, Bernard Henri
This paper concerns sparse decomposition of a noisy signal into atoms which are specified by unknown continuous-valued parameters. An example could be estimation of the model order, frequencies and amplitudes of a superposition of complex sinusoids. The common approach is to reduce the continuous...
Droplet Image Super Resolution Based on Sparse Representation and Kernel Regression
Zou, Zhenzhen; Luo, Xinghong; Yu, Qiang
Microgravity and containerless conditions, which are produced via electrostatic levitation combined with a drop tube, are important when studying the intrinsic properties of new metastable materials. Generally, temperature and image sensors can be used to measure the changes of sample temperature, morphology and volume. Then, the specific heat, surface tension, viscosity changes and sample density can be obtained. Considering that the falling speed of the material sample droplet is approximately 31.3 m/s when it reaches the bottom of a 50-meter-high drop tube, a high-speed camera with a collection rate of up to 106 frames/s is required to image the falling droplet. However, at the high-speed mode, very few pixels, approximately 48-120, will be obtained in each exposure time, which results in low image quality. Super-resolution image reconstruction is an algorithm that provides finer details than the sampling grid of a given imaging device by increasing the number of pixels per unit area in the image. In this work, we demonstrate the application of single image-resolution reconstruction in the microgravity and electrostatic levitation for the first time. Here, using the image super-resolution method based on sparse representation, a low-resolution droplet image can be reconstructed. Employed Yang's related dictionary model, high- and low-resolution image patches were combined with dictionary training, and high- and low-resolution-related dictionaries were obtained. The online double-sparse dictionary training algorithm was used in the study of related dictionaries and overcome the shortcomings of the traditional training algorithm with small image patch. During the stage of image reconstruction, the algorithm of kernel regression is added, which effectively overcomes the shortcomings of the Yang image's edge blurs.
Sparse regularization for EIT reconstruction incorporating structural information derived from medical imaging.
Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Mueller-Lisse, Ullrich; Moeller, Knut
Electrical impedance tomography (EIT) reconstructs the conductivity distribution of a domain using electrical data on its boundary. This is an ill-posed inverse problem usually solved on a finite element mesh. For this article, a special regularization method incorporating structural information of the targeted domain is proposed and evaluated. Structural information was obtained either from computed tomography images or from preliminary EIT reconstructions by a modified k-means clustering. The proposed regularization method integrates this structural information into the reconstruction as a soft constraint preferring sparsity in group level. A first evaluation with Monte Carlo simulations indicated that the proposed solver is more robust to noise and the resulting images show fewer artifacts. This finding is supported by real data analysis. The structure based regularization has the potential to balance structural a priori information with data driven reconstruction. It is robust to noise, reduces artifacts and produces images that reflect anatomy and are thus easier to interpret for physicians.
PARAMETER ESTIMATION AND MODEL SELECTION FOR INDOOR ENVIRONMENTS BASED ON SPARSE OBSERVATIONS
Y. Dehbi
Full Text Available This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed.
Dehbi, Y.; Loch-Dehbi, S.; Plümer, L.
This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed.
Tensor-based Dictionary Learning for Spectral CT Reconstruction
Zhang, Yanbo; Wang, Ge
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628
Tensor-Based Dictionary Learning for Spectral CT Reconstruction.
Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.
Low-Dose X-ray CT Reconstruction via Dictionary Learning
Xu, Qiong; Zhang, Lei; Hsieh, Jiang; Wang, Ge
Although diagnostic medical imaging provides enormous benefits in the early detection and accuracy diagnosis of various diseases, there are growing concerns on the potential side effect of radiation induced genetic, cancerous and other diseases. How to reduce radiation dose while maintaining the diagnostic performance is a major challenge in the computed tomography (CT) field. Inspired by the compressive sensing theory, the sparse constraint in terms of total variation (TV) minimization has already led to promising results for low-dose CT reconstruction. Compared to the discrete gradient transform used in the TV method, dictionary learning is proven to be an effective way for sparse representation. On the other hand, it is important to consider the statistical property of projection data in the low-dose CT case. Recently, we have developed a dictionary learning based approach for low-dose X-ray CT. In this paper, we present this method in detail and evaluate it in experiments. In our method, the sparse constraint in terms of a redundant dictionary is incorporated into an objective function in a statistical iterative reconstruction framework. The dictionary can be either predetermined before an image reconstruction task or adaptively defined during the reconstruction process. An alternating minimization scheme is developed to minimize the objective function. Our approach is evaluated with low-dose X-ray projections collected in animal and human CT studies, and the improvement associated with dictionary learning is quantified relative to filtered backprojection and TV-based reconstructions. The results show that the proposed approach might produce better images with lower noise and more detailed structural features in our selected cases. However, there is no proof that this is true for all kinds of structures. PMID:22542666
Thin-film sparse boundary array design for passive acoustic mapping during ultrasound therapy.
Coviello, Christian M; Kozick, Richard J; Hurrell, Andrew; Smith, Penny Probert; Coussios, Constantin-C
A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array's geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology.
Sparse Channel Estimation for MIMO-OFDM Two-Way Relay Network with Compressed Sensing
Aihua Zhang
Full Text Available Accurate channel impulse response (CIR is required for equalization and can help improve communication service quality in next-generation wireless communication systems. An example of an advanced system is amplify-and-forward multiple-input multiple-output two-way relay network, which is modulated by orthogonal frequency-division multiplexing. Linear channel estimation methods, for example, least squares and expectation conditional maximization, have been proposed previously for the system. However, these methods do not take advantage of channel sparsity, and they decrease estimation performance. We propose a sparse channel estimation scheme, which is different from linear methods, at end users under the relay channel to enable us to exploit sparsity. First, we formulate the sparse channel estimation problem as a compressed sensing problem by using sparse decomposition theory. Second, the CIR is reconstructed by CoSaMP and OMP algorithms. Finally, computer simulations are conducted to confirm the superiority of the proposed methods over traditional linear channel estimation methods.
Example-Based Image Colorization Using Locality Consistent Sparse Representation.
Bo Li; Fuchen Zhao; Zhuo Su; Xiangguo Liang; Yu-Kun Lai; Rosin, Paul L
Image colorization aims to produce a natural looking color image from a given gray-scale image, which remains a challenging problem. In this paper, we propose a novel example-based image colorization method exploiting a new locality consistent sparse representation. Given a single reference color image, our method automatically colorizes the target gray-scale image by sparse pursuit. For efficiency and robustness, our method operates at the superpixel level. We extract low-level intensity features, mid-level texture features, and high-level semantic features for each superpixel, which are then concatenated to form its descriptor. The collection of feature vectors for all the superpixels from the reference image composes the dictionary. We formulate colorization of target superpixels as a dictionary-based sparse reconstruction problem. Inspired by the observation that superpixels with similar spatial location and/or feature representation are likely to match spatially close regions from the reference image, we further introduce a locality promoting regularization term into the energy formulation, which substantially improves the matching consistency and subsequent colorization results. Target superpixels are colorized based on the chrominance information from the dominant reference superpixels. Finally, to further improve coherence while preserving sharpness, we develop a new edge-preserving filter for chrominance channels with the guidance from the target gray-scale image. To the best of our knowledge, this is the first work on sparse pursuit image colorization from single reference images. Experimental results demonstrate that our colorization method outperforms the state-of-the-art methods, both visually and quantitatively using a user study.
DOLPHIn—Dictionary Learning for Phase Retrieval
Tillmann, Andreas M.; Eldar, Yonina C.; Mairal, Julien
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method.
Sparse representation and dictionary learning penalized image reconstruction for positron emission tomography
Chen, Shuhang; Liu, Huafeng; Shi, Pengcheng; Chen, Yunmei
Accurate and robust reconstruction of the radioactivity concentration is of great importance in positron emission tomography (PET) imaging. Given the Poisson nature of photo-counting measurements, we present a reconstruction framework that integrates sparsity penalty on a dictionary into a maximum likelihood estimator. Patch-sparsity on a dictionary provides the regularization for our effort, and iterative procedures are used to solve the maximum likelihood function formulated on Poisson statistics. Specifically, in our formulation, a dictionary could be trained on CT images, to provide intrinsic anatomical structures for the reconstructed images, or adaptively learned from the noisy measurements of PET. Accuracy of the strategy with very promising application results from Monte-Carlo simulations, and real data are demonstrated. (paper)
Image Super-Resolution Algorithm Based on an Improved Sparse Autoencoder
Detian Huang
Full Text Available Due to the limitations of the resolution of the imaging system and the influence of scene changes and other factors, sometimes only low-resolution images can be acquired, which cannot satisfy the practical application's requirements. To improve the quality of low-resolution images, a novel super-resolution algorithm based on an improved sparse autoencoder is proposed. Firstly, in the training set preprocessing stage, the high- and low-resolution image training sets are constructed, respectively, by using high-frequency information of the training samples as the characterization, and then the zero-phase component analysis whitening technique is utilized to decorrelate the formed joint training set to reduce its redundancy. Secondly, a constructed sparse regularization term is added to the cost function of the traditional sparse autoencoder to further strengthen the sparseness constraint on the hidden layer. Finally, in the dictionary learning stage, the improved sparse autoencoder is adopted to achieve unsupervised dictionary learning to improve the accuracy and stability of the dictionary. Experimental results validate that the proposed algorithm outperforms the existing algorithms both in terms of the subjective visual perception and the objective evaluation indices, including the peak signal-to-noise ratio and the structural similarity measure.
SIRFING: Sparse Image Reconstruction For INterferometry using GPUs
Cranmer, Miles; Garsden, Hugh; Mitchell, Daniel A.; Greenhill, Lincoln
We present a deconvolution code for radio interferometric imaging based on the compressed sensing algorithms in Garsden et al. (2015). Being computationally intensive, compressed sensing is ripe for parallelization over GPUs. Our compressed sensing implementation generates images using wavelets, and we have ported the underlying wavelet library to CUDA, targeting the spline filter reconstruction part of the algorithm. The speedup achieved is almost an order of magnitude. The code is modular but is also being integrated into the calibration and imaging pipeline in use by the LEDA project at the Long Wavelength Array (LWA) as well as by the Murchinson Widefield Array (MWA).
Fully three-dimensional image reconstruction in radiology and nuclear medicine. Proceedings
The proceedings of the meeting on ''fully three-dimensional image reconstruction in radiology and nuclear medicine'' covers contributions on the following topics: CT imaging, PET imaging, fidelity; iterative and few-view CT, CT-analytical; PET/SPECT Compton analytical; doses - spectral methods; phase contrast; compressed sensing- sparse reconstruction; special issues; motion - cardiac.
Sparse Representation Denoising for Radar High Resolution Range Profiling
Min Li
Full Text Available Radar high resolution range profile has attracted considerable attention in radar automatic target recognition. In practice, radar return is usually contaminated by noise, which results in profile distortion and recognition performance degradation. To deal with this problem, in this paper, a novel denoising method based on sparse representation is proposed to remove the Gaussian white additive noise. The return is sparsely described in the Fourier redundant dictionary and the denoising problem is described as a sparse representation model. Noise level of the return, which is crucial to the denoising performance but often unknown, is estimated by performing subspace method on the sliding subsequence correlation matrix. Sliding window process enables noise level estimation using only one observation sequence, not only guaranteeing estimation efficiency but also avoiding the influence of profile time-shift sensitivity. Experimental results show that the proposed method can effectively improve the signal-to-noise ratio of the return, leading to a high-quality profile.
TH-AB-202-08: A Robust Real-Time Surface Reconstruction Method On Point Clouds Captured From a 3D Surface Photogrammetry System
Liu, W; Sawant, A; Ruan, D
Purpose: Surface photogrammetry (e.g. VisionRT, C-Rad) provides a noninvasive way to obtain high-frequency measurement for patient motion monitoring in radiotherapy. This work aims to develop a real-time surface reconstruction method on the acquired point clouds, whose acquisitions are subject to noise and missing measurements. In contrast to existing surface reconstruction methods that are usually computationally expensive, the proposed method reconstructs continuous surfaces with comparable accuracy in real-time. Methods: The key idea in our method is to solve and propagate a sparse linear relationship from the point cloud (measurement) manifold to the surface (reconstruction) manifold, taking advantage of the similarity in local geometric topology in both manifolds. With consistent point cloud acquisition, we propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, building the point correspondences by the iterative closest point (ICP) method. To accommodate changing noise levels and/or presence of inconsistent occlusions, we further propose a modified sparse regression (MSR) model to account for the large and sparse error built by ICP, with a Laplacian prior. We evaluated our method on both clinical acquired point clouds under consistent conditions and simulated point clouds with inconsistent occlusions. The reconstruction accuracy was evaluated w.r.t. root-mean-squared-error, by comparing the reconstructed surfaces against those from the variational reconstruction method. Results: On clinical point clouds, both the SR and MSR models achieved sub-millimeter accuracy, with mean reconstruction time reduced from 82.23 seconds to 0.52 seconds and 0.94 seconds, respectively. On simulated point cloud with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent performance despite the introduced occlusions. Conclusion: We have developed a real
A novel algorithm of super-resolution image reconstruction based on multi-class dictionaries for natural scene
Wu, Wei; Zhao, Dewei; Zhang, Huan
Super-resolution image reconstruction is an effective method to improve the image quality. It has important research significance in the field of image processing. However, the choice of the dictionary directly affects the efficiency of image reconstruction. A sparse representation theory is introduced into the problem of the nearest neighbor selection. Based on the sparse representation of super-resolution image reconstruction method, a super-resolution image reconstruction algorithm based on multi-class dictionary is analyzed. This method avoids the redundancy problem of only training a hyper complete dictionary, and makes the sub-dictionary more representatives, and then replaces the traditional Euclidean distance computing method to improve the quality of the whole image reconstruction. In addition, the ill-posed problem is introduced into non-local self-similarity regularization. Experimental results show that the algorithm is much better results than state-of-the-art algorithm in terms of both PSNR and visual perception.
Improved statistical power with a sparse shape model in detecting an aging effect in the hippocampus and amygdala
Chung, Moo K.; Kim, Seung-Goo; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matthew J.; Davidson, Richard J.
The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.
Regularized non-stationary morphological reconstruction algorithm for weak signal detection in microseismic monitoring: methodology
Huang, Weilin; Wang, Runqiu; Chen, Yangkang
Microseismic signal is typically weak compared with the strong background noise. In order to effectively detect the weak signal in microseismic data, we propose a mathematical morphology based approach. We decompose the initial data into several morphological multiscale components. For detection of weak signal, a non-stationary weighting operator is proposed and introduced into the process of reconstruction of data by morphological multiscale components. The non-stationary weighting operator can be obtained by solving an inversion problem. The regularized non-stationary method can be understood as a non-stationary matching filtering method, where the matching filter has the same size as the data to be filtered. In this paper, we provide detailed algorithmic descriptions and analysis. The detailed algorithm framework, parameter selection and computational issue for the regularized non-stationary morphological reconstruction (RNMR) method are presented. We validate the presented method through a comprehensive analysis through different data examples. We first test the proposed technique using a synthetic data set. Then the proposed technique is applied to a field project, where the signals induced from hydraulic fracturing are recorded by 12 three-component geophones in a monitoring well. The result demonstrates that the RNMR can improve the detectability of the weak microseismic signals. Using the processed data, the short-term-average over long-term average picking algorithm and Geiger's method are applied to obtain new locations of microseismic events. In addition, we show that the proposed RNMR method can be used not only in microseismic data but also in reflection seismic data to detect the weak signal. We also discussed the extension of RNMR from 1-D to 2-D or a higher dimensional version.
A Complete Readout Chain of the ATLAS Tile Calorimeter for the HL-LHC: from FATALIC Front-End Electronics to Signal Reconstruction
Senkin, Sergey; The ATLAS collaboration
The ATLAS Collaboration has started a vast programme of upgrades in the context of high-luminosity LHC (HL-LHC) foreseen in 2024. We present here one of the front-end readout options, an ASIC called FATALIC, which is proposed for the high-luminosity phase LHC upgrade of the ATLAS Tile Calorimeter. Based on a 130 nm CMOS technology, FATALIC performs the complete signal processing, including amplification, shaping and digitisation. Hereby we describe the full characterisation of FATALIC and also the signal reconstruction up to the observables of interest for physics: the energy and the arrival time of the particle. The Optimal Filtering signal reconstruction method is adapted to fully exploit the FATALIC three-range layout. Additionally, we present the performance in terms of resolution of the whole chain measured using the charge injection system designed for calibration. Finally, the results of the signal reconstruction used on real data collected during a preliminary beam test at CERN are discussed.
A comparison of reconstruction methods for undersampled atomic force microscopy images
Luo, Yufan; Andersson, Sean B
Non-raster scanning and undersampling of atomic force microscopy (AFM) images is a technique for improving imaging rate and reducing the amount of tip–sample interaction needed to produce an image. Generation of the final image can be done using a variety of image processing techniques based on interpolation or optimization. The choice of reconstruction method has a large impact on the quality of the recovered image and the proper choice depends on the sample under study. In this work we compare interpolation through the use of inpainting algorithms with reconstruction based on optimization through the use of the basis pursuit algorithm commonly used for signal recovery in compressive sensing. Using four different sampling patterns found in non-raster AFM, namely row subsampling, spiral scanning, Lissajous scanning, and random scanning, we subsample data from existing images and compare reconstruction performance against the original image. The results illustrate that inpainting generally produces superior results when the image contains primarily low frequency content while basis pursuit is better when the images have mixed, but sparse, frequency content. Using support vector machines, we then classify images based on their frequency content and sparsity and, from this classification, develop a fast decision strategy to select a reconstruction algorithm to be used on subsampled data. The performance of the classification and decision test are demonstrated on test AFM images. (paper)
The Real-Valued Sparse Direction of Arrival (DOA Estimation Based on the Khatri-Rao Product
Tao Chen
Full Text Available There is a problem that complex operation which leads to a heavy calculation burden is required when the direction of arrival (DOA of a sparse signal is estimated by using the array covariance matrix. The solution of the multiple measurement vectors (MMV model is difficult. In this paper, a real-valued sparse DOA estimation algorithm based on the Khatri-Rao (KR product called the L1-RVSKR is proposed. The proposed algorithm is based on the sparse representation of the array covariance matrix. The array covariance matrix is transformed to a real-valued matrix via a unitary transformation so that a real-valued sparse model is achieved. The real-valued sparse model is vectorized for transforming to a single measurement vector (SMV model, and a new virtual overcomplete dictionary is constructed according to the KR product's property. Finally, the sparse DOA estimation is solved by utilizing the idea of a sparse representation of array covariance vectors (SRACV. The simulation results demonstrate the superior performance and the low computational complexity of the proposed algorithm.
Group-sparse representation with dictionary learning for medical image denoising and fusion.
Li, Shutao; Yin, Haitao; Fang, Leyuan
Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.
A Comparison of Compressed Sensing and Sparse Recovery Algorithms Applied to Simulation Data
Ya Ju Fan
Full Text Available The move toward exascale computing for scientific simulations is placing new demands on compression techniques. It is expected that the I/O system will not be able to support the volume of data that is expected to be written out. To enable quantitative analysis and scientific discovery, we are interested in techniques that compress high-dimensional simulation data and can provide perfect or near-perfect reconstruction. In this paper, we explore the use of compressed sensing (CS techniques to reduce the size of the data before they are written out. Using large-scale simulation data, we investigate how the sufficient sparsity condition and the contrast in the data affect the quality of reconstruction and the degree of compression. We provide suggestions for the practical implementation of CS techniques and compare them with other sparse recovery methods. Our results show that despite longer times for reconstruction, compressed sensing techniques can provide near perfect reconstruction over a range of data with varying sparsity.
Reconstruction of signal in plastic scintillator of PET using Tikhonov regularization.
Raczynski, Lech
The new concept of Time of Flight Positron Emission Tomography (TOF-PET) detection system, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The Jagiellonian-PET (J-PET) detector improves the TOF resolution due to the use of fast plastic scintillators. Since registration of the waveform of signals with duration times of few nanoseconds is not feasible, a novel front-end electronics allowing for sampling in a voltage domain at four thresholds was developed. To take fully advantage of these fast signals a novel scheme of recovery of the waveform of the signal, based on idea from the Tikhonov regularization method, is presented. From the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This step is crucial to introduce and prove the formula for calculations of the signal recovery error. The method is tested using signals registered by means of the single detection module of the J-PET detector built out from the 30 cm long plastic scintillator strip. It is shown that using the recovered waveform of the signals, instead of samples at four voltage levels alone, improves the spatial resolution of the hit position reconstruction from 1.05 cm to 0.94 cm. Moreover, the obtained result is only slightly worse than the one evaluated using the original raw-signal. The spatial resolution calculated under these conditions is equal to 0.93 cm.
Sparse Channel Estimation Including the Impact of the Transceiver Filters with Application to OFDM
Barbu, Oana-Elena; Pedersen, Niels Lovmand; Manchón, Carles Navarro
Traditionally, the dictionary matrices used in sparse wireless channel estimation have been based on the discrete Fourier transform, following the assumption that the channel frequency response (CFR) can be approximated as a linear combination of a small number of multipath components, each one......) and receive (demodulation) filters. Hence, the assumption of the CFR being sparse in the canonical Fourier dictionary may no longer hold. In this work, we derive a signal model and subsequently a novel dictionary matrix for sparse estimation that account for the impact of transceiver filters. Numerical...... results obtained in an OFDM transmission scenario demonstrate the superior accuracy of a sparse estimator that uses our proposed dictionary rather than the classical Fourier dictionary, and its robustness against a mismatch in the assumed transmit filter characteristics....
Reprint of "Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency".
Tensor-based dictionary learning for dynamic tomographic reconstruction
Tan, Shengqi; Wu, Zhifang; Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Cao, Guohua; Yu, Hengyong
In dynamic computed tomography (CT) reconstruction, the data acquisition speed limits the spatio-temporal resolution. Recently, compressed sensing theory has been instrumental in improving CT reconstruction from far few-view projections. In this paper, we present an adaptive method to train a tensor-based spatio-temporal dictionary for sparse representation of an image sequence during the reconstruction process. The correlations among atoms and across phases are considered to capture the characteristics of an object. The reconstruction problem is solved by the alternating direction method of multipliers. To recover fine or sharp structures such as edges, the nonlocal total variation is incorporated into the algorithmic framework. Preclinical examples including a sheep lung perfusion study and a dynamic mouse cardiac imaging demonstrate that the proposed approach outperforms the vectorized dictionary-based CT reconstruction in the case of few-view reconstruction. (paper)
Tan, Shengqi; Zhang, Yanbo; Wang, Ge; Mou, Xuanqin; Cao, Guohua; Wu, Zhifang; Yu, Hengyong
In dynamic computed tomography (CT) reconstruction, the data acquisition speed limits the spatio-temporal resolution. Recently, compressed sensing theory has been instrumental in improving CT reconstruction from far few-view projections. In this paper, we present an adaptive method to train a tensor-based spatio-temporal dictionary for sparse representation of an image sequence during the reconstruction process. The correlations among atoms and across phases are considered to capture the characteristics of an object. The reconstruction problem is solved by the alternating direction method of multipliers. To recover fine or sharp structures such as edges, the nonlocal total variation is incorporated into the algorithmic framework. Preclinical examples including a sheep lung perfusion study and a dynamic mouse cardiac imaging demonstrate that the proposed approach outperforms the vectorized dictionary-based CT reconstruction in the case of few-view reconstruction. PMID:25779991
Dentate Gyrus circuitry features improve performance of sparse approximation algorithms.
Panagiotis C Petrantonakis
Full Text Available Memory-related activity in the Dentate Gyrus (DG is characterized by sparsity. Memory representations are seen as activated neuronal populations of granule cells, the main encoding cells in DG, which are estimated to engage 2-4% of the total population. This sparsity is assumed to enhance the ability of DG to perform pattern separation, one of the most valuable contributions of DG during memory formation. In this work, we investigate how features of the DG such as its excitatory and inhibitory connectivity diagram can be used to develop theoretical algorithms performing Sparse Approximation, a widely used strategy in the Signal Processing field. Sparse approximation stands for the algorithmic identification of few components from a dictionary that approximate a certain signal. The ability of DG to achieve pattern separation by sparsifing its representations is exploited here to improve the performance of the state of the art sparse approximation algorithm "Iterative Soft Thresholding" (IST by adding new algorithmic features inspired by the DG circuitry. Lateral inhibition of granule cells, either direct or indirect, via mossy cells, is shown to enhance the performance of the IST. Apart from revealing the potential of DG-inspired theoretical algorithms, this work presents new insights regarding the function of particular cell types in the pattern separation task of the DG.
Sparse Reconstruction of Electric Fields from Radial Magnetic Data
Yeates, Anthony R.
Accurate estimates of the horizontal electric field on the Sun's visible surface are important not only for estimating the Poynting flux of magnetic energy into the corona but also for driving time-dependent magnetohydrodynamic models of the corona. In this paper, a method is developed for estimating the horizontal electric field from a sequence of radial-component magnetic field maps. This problem of inverting Faraday's law has no unique solution. Unfortunately, the simplest solution (a divergence-free electric field) is not realistically localized in regions of nonzero magnetic field, as would be expected from Ohm's law. Our new method generates instead a localized solution, using a basis pursuit algorithm to find a sparse solution for the electric field. The method is shown to perform well on test cases where the input magnetic maps are flux balanced in both Cartesian and spherical geometries. However, we show that if the input maps have a significant imbalance of flux—usually arising from data assimilation—then it is not possible to find a localized, realistic, electric field solution. This is the main obstacle to driving coronal models from time sequences of solar surface magnetic maps.
Yeates, Anthony R. [Department of Mathematical Sciences, Durham University, Durham, DH1 3LE (United Kingdom)
Sparse orthogonal population representation of spatial context in the retrosplenial cortex.
Mao, Dun; Kandler, Steffen; McNaughton, Bruce L; Bonin, Vincent
Sparse orthogonal coding is a key feature of hippocampal neural activity, which is believed to increase episodic memory capacity and to assist in navigation. Some retrosplenial cortex (RSC) neurons convey distributed spatial and navigational signals, but place-field representations such as observed in the hippocampus have not been reported. Combining cellular Ca 2+ imaging in RSC of mice with a head-fixed locomotion assay, we identified a population of RSC neurons, located predominantly in superficial layers, whose ensemble activity closely resembles that of hippocampal CA1 place cells during the same task. Like CA1 place cells, these RSC neurons fire in sequences during movement, and show narrowly tuned firing fields that form a sparse, orthogonal code correlated with location. RSC 'place' cell activity is robust to environmental manipulations, showing partial remapping similar to that observed in CA1. This population code for spatial context may assist the RSC in its role in memory and/or navigation.Neurons in the retrosplenial cortex (RSC) encode spatial and navigational signals. Here the authors use calcium imaging to show that, similar to the hippocampus, RSC neurons also encode place cell-like activity in a sparse orthogonal representation, partially anchored to the allocentric cues on the linear track.
Comprehensive quantification of signal-to-noise ratio and g-factor for image-based and k-space-based parallel imaging reconstructions.
Robson, Philip M; Grant, Aaron K; Madhuranthakam, Ananth J; Lattanzi, Riccardo; Sodickson, Daniel K; McKenzie, Charles A
Parallel imaging reconstructions result in spatially varying noise amplification characterized by the g-factor, precluding conventional measurements of noise from the final image. A simple Monte Carlo based method is proposed for all linear image reconstruction algorithms, which allows measurement of signal-to-noise ratio and g-factor and is demonstrated for SENSE and GRAPPA reconstructions for accelerated acquisitions that have not previously been amenable to such assessment. Only a simple "prescan" measurement of noise amplitude and correlation in the phased-array receiver, and a single accelerated image acquisition are required, allowing robust assessment of signal-to-noise ratio and g-factor. The "pseudo multiple replica" method has been rigorously validated in phantoms and in vivo, showing excellent agreement with true multiple replica and analytical methods. This method is universally applicable to the parallel imaging reconstruction techniques used in clinical applications and will allow pixel-by-pixel image noise measurements for all parallel imaging strategies, allowing quantitative comparison between arbitrary k-space trajectories, image reconstruction, or noise conditioning techniques. (c) 2008 Wiley-Liss, Inc.
Narrowband interference parameterization for sparse Bayesian recovery
This paper addresses the problem of narrowband interference (NBI) in SC-FDMA systems by using tools from compressed sensing and stochastic geometry. The proposed NBI cancellation scheme exploits the frequency domain sparsity of the unknown signal and adopts a Bayesian sparse recovery procedure. This is done by keeping a few randomly chosen sub-carriers data free to sense the NBI signal at the receiver. As Bayesian recovery requires knowledge of some NBI parameters (i.e., mean, variance and sparsity rate), we use tools from stochastic geometry to obtain analytical expressions for the required parameters. Our simulation results validate the analysis and depict suitability of the proposed recovery method for NBI mitigation. © 2015 IEEE.
Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging
synthetically generated or actually measured scattered fields, show that the images recovered by these sparsity-regularized methods are sharper and more accurate than those produced by existing methods. The methods developed in this work have potential application areas ranging from oil/gas reservoir engineering to biological imaging where sparse domains naturally exist.
Adaptive tight frame based medical image reconstruction: a proof-of-concept study for computed tomography
Zhou, Weifeng; Cai, Jian-Feng; Gao, Hao
A popular approach for medical image reconstruction has been through the sparsity regularization, assuming the targeted image can be well approximated by sparse coefficients under some properly designed system. The wavelet tight frame is such a widely used system due to its capability for sparsely approximating piecewise-smooth functions, such as medical images. However, using a fixed system may not always be optimal for reconstructing a variety of diversified images. Recently, the method based on the adaptive over-complete dictionary that is specific to structures of the targeted images has demonstrated its superiority for image processing. This work is to develop the adaptive wavelet tight frame method image reconstruction. The proposed scheme first constructs the adaptive wavelet tight frame that is task specific, and then reconstructs the image of interest by solving an l 1 -regularized minimization problem using the constructed adaptive tight frame system. The proof-of-concept study is performed for computed tomography (CT), and the simulation results suggest that the adaptive tight frame method improves the reconstructed CT image quality from the traditional tight frame method. (paper)
Noise and signal properties in PSF-based fully 3D PET image reconstruction: an experimental evaluation
Tong, S; Alessio, A M; Kinahan, P E
The addition of accurate system modeling in PET image reconstruction results in images with distinct noise texture and characteristics. In particular, the incorporation of point spread functions (PSF) into the system model has been shown to visually reduce image noise, but the noise properties have not been thoroughly studied. This work offers a systematic evaluation of noise and signal properties in different combinations of reconstruction methods and parameters. We evaluate two fully 3D PET reconstruction algorithms: (1) OSEM with exact scanner line of response modeled (OSEM+LOR), (2) OSEM with line of response and a measured point spread function incorporated (OSEM+LOR+PSF), in combination with the effects of four post-reconstruction filtering parameters and 1-10 iterations, representing a range of clinically acceptable settings. We used a modified NEMA image quality (IQ) phantom, which was filled with 68 Ge and consisted of six hot spheres of different sizes with a target/background ratio of 4:1. The phantom was scanned 50 times in 3D mode on a clinical system to provide independent noise realizations. Data were reconstructed with OSEM+LOR and OSEM+LOR+PSF using different reconstruction parameters, and our implementations of the algorithms match the vendor's product algorithms. With access to multiple realizations, background noise characteristics were quantified with four metrics. Image roughness and the standard deviation image measured the pixel-to-pixel variation; background variability and ensemble noise quantified the region-to-region variation. Image roughness is the image noise perceived when viewing an individual image. At matched iterations, the addition of PSF leads to images with less noise defined as image roughness (reduced by 35% for unfiltered data) and as the standard deviation image, while it has no effect on background variability or ensemble noise. In terms of signal to noise performance, PSF-based reconstruction has a 7% improvement in
High efficient optical remote sensing images acquisition for nano-satellite: reconstruction algorithms
Liu, Yang; Li, Feng; Xin, Lei; Fu, Jie; Huang, Puming
Large amount of data is one of the most obvious features in satellite based remote sensing systems, which is also a burden for data processing and transmission. The theory of compressive sensing(CS) has been proposed for almost a decade, and massive experiments show that CS has favorable performance in data compression and recovery, so we apply CS theory to remote sensing images acquisition. In CS, the construction of classical sensing matrix for all sparse signals has to satisfy the Restricted Isometry Property (RIP) strictly, which limits applying CS in practical in image compression. While for remote sensing images, we know some inherent characteristics such as non-negative, smoothness and etc.. Therefore, the goal of this paper is to present a novel measurement matrix that breaks RIP. The new sensing matrix consists of two parts: the standard Nyquist sampling matrix for thumbnails and the conventional CS sampling matrix. Since most of sun-synchronous based satellites fly around the earth 90 minutes and the revisit cycle is also short, lots of previously captured remote sensing images of the same place are available in advance. This drives us to reconstruct remote sensing images through a deep learning approach with those measurements from the new framework. Therefore, we propose a novel deep convolutional neural network (CNN) architecture which takes in undersampsing measurements as input and outputs an intermediate reconstruction image. It is well known that the training procedure to the network costs long time, luckily, the training step can be done only once, which makes the approach attractive for a host of sparse recovery problems.
A reliability index for assessment of crack profile reconstructed from ECT signals using a neural-network approach
Yusa, Noritaka; Chen, Zhenmao; Miya, Kenzo; Cheng, Weiying
This paper proposes a reliability parameter to enhance an version scheme developed by authors. The scheme is based upon an artificial neural network that simulates mapping between eddy current signals and crack profiles. One of the biggest advantages of the scheme is that it can deal with conductive cracks, which is necessary to reconstruct natural cracks. However, it has one significant disadvantage: the reliability of reconstructed profiles was unknown. The parameter provides an index for assessment of the crack profile and overcomes this disadvantage. After the parameter is validated by reconstruction of simulated cracks, it is applied to reconstruction of natural cracks that occurred in steam generator tubes of a pressurized water reactor. It is revealed that the parameter is applicable to not only simulated cracks but also natural ones. (author)
3D reconstruction based on light field images
Zhu, Dong; Wu, Chunhong; Liu, Yunluo; Fu, Dongmei
This paper proposed a method of reconstructing three-dimensional (3D) scene from two light field images capture by Lytro illium. The work was carried out by first extracting the sub-aperture images from light field images and using the scale-invariant feature transform (SIFT) for feature registration on the selected sub-aperture images. Structure from motion (SFM) algorithm is further used on the registration completed sub-aperture images to reconstruct the three-dimensional scene. 3D sparse point cloud was obtained in the end. The method shows that the 3D reconstruction can be implemented by only two light field camera captures, rather than at least a dozen times captures by traditional cameras. This can effectively solve the time-consuming, laborious issues for 3D reconstruction based on traditional digital cameras, to achieve a more rapid, convenient and accurate reconstruction.
New trends in applied harmonic analysis sparse representations, compressed sensing, and multifractal analysis
Cabrelli, Carlos; Jaffard, Stephane; Molter, Ursula
This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and covers both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.
Photoacoustic image reconstruction via deep learning
Antholzer, Stephan; Haltmeier, Markus; Nuster, Robert; Schwab, Johannes
Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction algorithms which allow to include prior knowledge such as smoothness, total variation (TV) or sparsity constraints. These algorithms tend to be time consuming as the forward and adjoint problems have to be solved repeatedly. Further, iterative algorithms have additional drawbacks. For example, the reconstruction quality strongly depends on a-priori model assumptions about the objects to be recovered, which are often not strictly satisfied in practical applications. To overcome these issues, in this paper, we develop direct and efficient reconstruction algorithms based on deep learning. As opposed to iterative algorithms, we apply a convolutional neural network, whose parameters are trained before the reconstruction process based on a set of training data. For actual image reconstruction, a single evaluation of the trained network yields the desired result. Our presented numerical results (using two different network architectures) demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative reconstruction methods.
Signal Separation of Helicopter Radar Returns Using Wavelet-Based Sparse Signal Optimisation
helicopter from the composite radar returns. The received signal consists of returns from the rotating main and tail rotor blades, the helicopter body...is used to separate the main and tail rotor blade components of a helicopter from the composite radar returns. The received signal consists of returns...Two algorithms are presented in the report to separately extract main rotor blade returns and tail rotor blade returns from the composite signal
Enhancement of snow cover change detection with sparse representation and dictionary learning
Varade, D.; Dikshit, O.
Sparse representation and decoding is often used for denoising images and compression of images with respect to inherent features. In this paper, we adopt a methodology incorporating sparse representation of a snow cover change map using the K-SVD trained dictionary and sparse decoding to enhance the change map. The pixels often falsely characterized as "changes" are eliminated using this approach. The preliminary change map was generated using differenced NDSI or S3 maps in case of Resourcesat-2 and Landsat 8 OLI imagery respectively. These maps are extracted into patches for compressed sensing using Discrete Cosine Transform (DCT) to generate an initial dictionary which is trained by the K-SVD approach. The trained dictionary is used for sparse coding of the change map using the Orthogonal Matching Pursuit (OMP) algorithm. The reconstructed change map incorporates a greater degree of smoothing and represents the features (snow cover changes) with better accuracy. The enhanced change map is segmented using kmeans to discriminate between the changed and non-changed pixels. The segmented enhanced change map is compared, firstly with the difference of Support Vector Machine (SVM) classified NDSI maps and secondly with a reference data generated as a mask by visual interpretation of the two input images. The methodology is evaluated using multi-spectral datasets from Resourcesat-2 and Landsat-8. The k-hat statistic is computed to determine the accuracy of the proposed approach.
Incremental Reconstruction of Urban Environments by Edge-Points Delaunay Triangulation
Romanoni, Andrea; Matteucci, Matteo
Urban reconstruction from a video captured by a surveying vehicle constitutes a core module of automated mapping. When computational power represents a limited resource and, a detailed map is not the primary goal, the reconstruction can be performed incrementally, from a monocular video, carving a 3D Delaunay triangulation of sparse points; this allows online incremental mapping for tasks such as traversability analysis or obstacle avoidance. To exploit the sharp edges of urban landscape, we ...
Inhibitory neurons modulate spontaneous signaling in cultured cortical neurons: density-dependent regulation of excitatory neuronal signaling
Serra, Michael; Guaraldi, Mary; Shea, Thomas B
Cortical neuronal activity depends on a balance between excitatory and inhibitory influences. Culturing of neurons on multi-electrode arrays (MEAs) has provided insight into the development and maintenance of neuronal networks. Herein, we seeded MEAs with murine embryonic cortical/hippocampal neurons at different densities ( 1000 cells mm −2 ) and monitored resultant spontaneous signaling. Sparsely seeded cultures displayed a large number of bipolar, rapid, high-amplitude individual signals with no apparent temporal regularity. By contrast, densely seeded cultures instead displayed clusters of signals at regular intervals. These patterns were observed even within thinner and thicker areas of the same culture. GABAergic neurons (25% of total neurons in our cultures) mediated the differential signal patterns observed above, since addition of the inhibitory antagonist bicuculline to dense cultures and hippocampal slice cultures induced the signal pattern characteristic of sparse cultures. Sparsely seeded cultures likely lacked sufficient inhibitory neurons to modulate excitatory activity. Differential seeding of MEAs can provide a unique model for analyses of pertubation in the interaction between excitatory and inhibitory function during aging and neuropathological conditions where dysregulation of GABAergic neurons is a significant component
Sparse Reconstruction of the Merging A520 Cluster System
Peel, Austin [Département d'Astrophysique, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette (France); Lanusse, François [McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 (United States); Starck, Jean-Luc, E-mail: austin.peel@cea.fr [Université Paris Diderot, AIM, Sorbonne Paris Cité, CEA, CNRS, F-91191 Gif-sur-Yvette (France)
Merging galaxy clusters present a unique opportunity to study the properties of dark matter in an astrophysical context. These are rare and extreme cosmic events in which the bulk of the baryonic matter becomes displaced from the dark matter halos of the colliding subclusters. Since all mass bends light, weak gravitational lensing is a primary tool to study the total mass distribution in such systems. Combined with X-ray and optical analyses, mass maps of cluster mergers reconstructed from weak-lensing observations have been used to constrain the self-interaction cross-section of dark matter. The dynamically complex Abell 520 (A520) cluster is an exceptional case, even among merging systems: multi-wavelength observations have revealed a surprising high mass-to-light concentration of dark mass, the interpretation of which is difficult under the standard assumption of effectively collisionless dark matter. We revisit A520 using a new sparsity-based mass-mapping algorithm to independently assess the presence of the puzzling dark core. We obtain high-resolution mass reconstructions from two separate galaxy shape catalogs derived from Hubble Space Telescope observations of the system. Our mass maps agree well overall with the results of previous studies, but we find important differences. In particular, although we are able to identify the dark core at a certain level in both data sets, it is at much lower significance than has been reported before using the same data. As we cannot confirm the detection in our analysis, we do not consider A520 as posing a significant challenge to the collisionless dark matter scenario.
Reconstruction of networks from one-step data by matching positions
Wu, Jianshe; Dang, Ni; Jiao, Yang
It is a challenge in estimating the topology of a network from short time series data. In this paper, matching positions is developed to reconstruct the topology of a network from only one-step data. We consider a general network model of coupled agents, in which the phase transformation of each node is determined by its neighbors. From the phase transformation information from one step to the next, the connections of the tail vertices are reconstructed firstly by the matching positions. Removing the already reconstructed vertices, and repeatedly reconstructing the connections of tail vertices, the topology of the entire network is reconstructed. For sparse scale-free networks with more than ten thousands nodes, we almost obtain the actual topology using only the one-step data in simulations.
Apparatus for tomography in which signal profiles gathered from divergent radiation can be reconstructed in signal profiles, each corresponding with a beam of parallel rays
A tomograph which is capable of gathering divergent radiations and reconstruct them in signal profiles or images each corresponding with a beam of parallel rays is discussed which may eliminate the interfering point dispersion function which normally occurs
Optimization of number and signal to noise ratio radiographs for defects 3D reconstruction in industrial control
Bruandet, J.-P.
Among numerous techniques for non-destructive evaluation (NOE), X-rays systems are well suited to inspect inner objects. Acquiring several radiographs of inspected objects under different points of view enables to recover a three dimensional structural information. In this NOE application, a tomographic testing is considered. This work deals with two tomographic testing optimizations in order to improve the characterization of defects that may occur into metallic welds. The first one consists in the optimization of the acquisition strategy. Because tomographic testing is made on-line, the total duration for image acquisition is fixed, limiting the number of available views. Hence, for a given acquisition duration, it is possible either to acquire a very limited number of radiographs with a good signal to noise ratio in each single acquisition or a larger number of radiographs with a limited signal to noise ratio. The second one consists in optimizing the 3D reconstruction algorithms from a limited number of cone-beam projections. To manage the lack of data, we first used algebraic reconstruction algorithms such as ART or regularized ICM. In terms of acquisition strategy optimization, an increase of the number of projections was proved to be valuable. Taking into account specific prior knowledge such as support constraint or physical noise model in attenuation images also improved reconstruction quality. Then, a new regularized region based reconstruction approach was developed. Defects to reconstruct are binary (lack of material in a homogeneous object). As a consequence, they are entirely described by their shapes. Because the number of defects to recover is unknown and is totally arbitrary, a level set formulation allowing handling topological changes was used. Results obtained with a regularized level-set reconstruction algorithm are optimistic in the proposed context. (author) [fr
Sparse dynamical Boltzmann machine for reconstructing complex networks with binary dynamics
Chen, Yu-Zhong; Lai, Ying-Cheng
Revealing the structure and dynamics of complex networked systems from observed data is a problem of current interest. Is it possible to develop a completely data-driven framework to decipher the network structure and different types of dynamical processes on complex networks? We develop a model named sparse dynamical Boltzmann machine (SDBM) as a structural estimator for complex networks that host binary dynamical processes. The SDBM attains its topology according to that of the original system and is capable of simulating the original binary dynamical process. We develop a fully automated method based on compressive sensing and a clustering algorithm to construct the SDBM. We demonstrate, for a variety of representative dynamical processes on model and real world complex networks, that the equivalent SDBM can recover the network structure of the original system and simulates its dynamical behavior with high precision.
Passive electromagnetic NDE for mechanical damage inspection by detecting leakage magnetic flux. (I. Reconstruction of magnetic charges from detected field signals)
Chen, Zhenmao; Aoto, Kazumi; Kato, Syoichi
In this report, reconstruction of magnetic charges induced by mechanical damages in a test piece of SUS304 stainless steel is performed as a part of efforts to establish a passive nondestructive testing method on the basis of the inspection of leakage magnetic field. The approach for solving this typical ill-posed inverse problem is selected as a way in the least square method category. Concerning the ill-poseness of the system of equations, an iteration algorithm is adopted to its solving in which the designations of initial profile, the weight coefficients and the total number of iterations are taken as means of regularization. From examples using simulated input data, it is verified that the approach gives good reconstruction results in case of signals with a relative high S/N ratio. For improving the robustness of the proposed method, a Galerkin procedure with base functions chosen as the Daubechies' wavelet is also introduced for discretizing the governing equation. By comparing the reconstruction results of the least square method and those using wavelet discretization, it is found that the wavelet used approach is more feasible in the inversion of noise polluted signals. Reconstruction of 1-D and 2-D magnetic charges with the least square strategy and reconstruction of an 1-D problem with the wavelet used method are carried out from both simulated and measured magnetic field signals which are used as the validation of the proposed inversion strategy. (author)
Signal Based Mixing Analysis for the magnetohydrodynamic mode reconstruction from homodyne microwave reflectometry
Ejiri, Akira; Sakakibara, Satoru; Kawahata, Kazuo.
A new method 'Signal Based Mixing Analysis', to extract the components which are coherent to a certain reference signal from a noisy signal, has been developed. The method is applied to homodyne microwave reflectometry to reconstruct the radial structure of a magnetohydrodynamic (MHD) mode in heliotron/torsatron Compact Helical System (CHS) [K. Matsuoka et al. Plasma Phys. Control. Nuclear Fusion Research 1988 Vol. 2, IAEA, Vienna 411 (1989)]. In CHS plasmas, MHD fluctuations measured with magnetic probes show bursts, in which the amplitude and frequency quasi-periodically vary. The signal based mixing analysis uses a set of functions which have the same amplitude and the harmonic frequency as those of the magnetic fluctuations. The product (mixing) of the signal of reflectometer and the functions yields the amplitude and phase of the coherent components. When the plasma density gradually increases, the measuring position moves radially outward. Thus, the radial structure of MHD modes can be obtained by this method. The analysis indicates several peaks and nodes inside the resonance surface of the MHD mode. In addition, the structure does not propagate radially during a burst. (author)
A leakage-free resonance sparse decomposition technique for bearing fault detection in gearboxes
Osman, Shazali; Wang, Wilson
Most of rotating machinery deficiencies are related to defects in rolling element bearings. Reliable bearing fault detection still remains a challenging task, especially for bearings in gearboxes as bearing-defect-related features are nonstationary and modulated by gear mesh vibration. A new leakage-free resonance sparse decomposition (LRSD) technique is proposed in this paper for early bearing fault detection of gearboxes. In the proposed LRSD technique, a leakage-free filter is suggested to remove strong gear mesh and shaft running signatures. A kurtosis and cosine distance measure is suggested to select appropriate redundancy r and quality factor Q. The signal residual is processed by signal sparse decomposition for highpass and lowpass resonance analysis to extract representative features for bearing fault detection. The effectiveness of the proposed technique is verified by a succession of experimental tests corresponding to different gearbox and bearing conditions.
Robust extraction of basis functions for simultaneous and proportional myoelectric control via sparse non-negative matrix factorization
Lin, Chuang; Wang, Binghui; Jiang, Ning; Farina, Dario
Objective. This paper proposes a novel simultaneous and proportional multiple degree of freedom (DOF) myoelectric control method for active prostheses. Approach. The approach is based on non-negative matrix factorization (NMF) of surface EMG signals with the inclusion of sparseness constraints. By applying a sparseness constraint to the control signal matrix, it is possible to extract the basis information from arbitrary movements (quasi-unsupervised approach) for multiple DOFs concurrently. Main Results. In online testing based on target hitting, able-bodied subjects reached a greater throughput (TP) when using sparse NMF (SNMF) than with classic NMF or with linear regression (LR). Accordingly, the completion time (CT) was shorter for SNMF than NMF or LR. The same observations were made in two patients with unilateral limb deficiencies. Significance. The addition of sparseness constraints to NMF allows for a quasi-unsupervised approach to myoelectric control with superior results with respect to previous methods for the simultaneous and proportional control of multi-DOF. The proposed factorization algorithm allows robust simultaneous and proportional control, is superior to previous supervised algorithms, and, because of minimal supervision, paves the way to online adaptation in myoelectric control.
Application Research of the Sparse Representation of Eigenvector on the PD Positioning in the Transformer Oil
Qing Xie
Full Text Available The partial discharge (PD detection of electrical equipment is important for the safe operation of power system. The ultrasonic signal generated by the PD in the oil is a broadband signal. However, most methods of the array signal processing are used for the narrowband signal at present, and the effect of some methods for processing wideband signals is not satisfactory. Therefore, it is necessary to find new broadband signal processing methods to improve detection ability of the PD source. In this paper, the direction of arrival (DOA estimation method based on sparse representation of eigenvector is proposed, and this method can further reduce the noise interference. Moreover, the simulation results show that this direction finding method is feasible for broadband signal and thus improve the following positioning accuracy of the three-array localization method. And experimental results verify that the direction finding method based on sparse representation of eigenvector is feasible for the ultrasonic array, which can achieve accurate estimation of direction of arrival and improve the following positioning accuracy. This can provide important guidance information for the equipment maintenance in the practical application.
Near-field acoustic holography using sparse regularization and compressive sampling principles.
Chardon, Gilles; Daudet, Laurent; Peillot, Antoine; Ollivier, François; Bertin, Nancy; Gribonval, Rémi
Regularization of the inverse problem is a complex issue when using near-field acoustic holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, alternative regularization schemes can be developed based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e., the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of compressive sampling; under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.
Reconstruction Algorithms in Undersampled AFM Imaging
Arildsen, Thomas; Oxvig, Christian Schou; Pedersen, Patrick Steffen
This paper provides a study of spatial undersampling in atomic force microscopy (AFM) imaging followed by different image reconstruction techniques based on sparse approximation as well as interpolation. The main reasons for using undersampling is that it reduces the path length and thereby...... the scanning time as well as the amount of interaction between the AFM probe and the specimen. It can easily be applied on conventional AFM hardware. Due to undersampling, it is then necessary to further process the acquired image in order to reconstruct an approximation of the image. Based on real AFM cell...... images, our simulations reveal that using a simple raster scanning pattern in combination with conventional image interpolation performs very well. Moreover, this combination enables a reduction by a factor 10 of the scanning time while retaining an average reconstruction quality around 36 dB PSNR...
Sparse structure regularized ranking
Wang, Jim Jing-Yan; Sun, Yijun; Gao, Xin
Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse
Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse structure, we assume that each multimedia object could be represented as a sparse linear combination of all other objects, and combination coefficients are regarded as a similarity measure between objects and used to regularize their ranking scores. Moreover, we propose to learn the sparse combination coefficients and the ranking scores simultaneously. A unified objective function is constructed with regard to both the combination coefficients and the ranking scores, and is optimized by an iterative algorithm. Experiments on two multimedia database retrieval data sets demonstrate the significant improvements of the propose algorithm over state-of-the-art ranking score learning algorithms.
Turbulent flows over sparse canopies
Sharma, Akshath; García-Mayoral, Ricardo
Turbulent flows over sparse and dense canopies exerting a similar drag force on the flow are investigated using Direct Numerical Simulations. The dense canopies are modelled using a homogeneous drag force, while for the sparse canopy, the geometry of the canopy elements is represented. It is found that on using the friction velocity based on the local shear at each height, the streamwise velocity fluctuations and the Reynolds stress within the sparse canopy are similar to those from a comparable smooth-wall case. In addition, when scaled with the local friction velocity, the intensity of the off-wall peak in the streamwise vorticity for sparse canopies also recovers a value similar to a smooth-wall. This indicates that the sparse canopy does not significantly disturb the near-wall turbulence cycle, but causes its rescaling to an intensity consistent with a lower friction velocity within the canopy. In comparison, the dense canopy is found to have a higher damping effect on the turbulent fluctuations. For the case of the sparse canopy, a peak in the spectral energy density of the wall-normal velocity, and Reynolds stress is observed, which may indicate the formation of Kelvin-Helmholtz-like instabilities. It is also found that a sparse canopy is better modelled by a homogeneous drag applied on the mean flow alone, and not the turbulent fluctuations.
Few-view image reconstruction with dual dictionaries
Lu Yang; Zhao Jun; Wang Ge
In this paper, we formulate the problem of computed tomography (CT) under sparsity and few-view constraints, and propose a novel algorithm for image reconstruction from few-view data utilizing the simultaneous algebraic reconstruction technique (SART) coupled with dictionary learning, sparse representation and total variation (TV) minimization on two interconnected levels. The main feature of our algorithm is the use of two dictionaries: a transitional dictionary for atom matching and a global dictionary for image updating. The atoms in the global and transitional dictionaries represent the image patches from high-quality and low-quality CT images, respectively. Experiments with simulated and real projections were performed to evaluate and validate the proposed algorithm. The results reconstructed using the proposed approach are significantly better than those using either SART or SART–TV. (paper)
Sinogram denoising via simultaneous sparse representation in learned dictionaries
Karimi, Davood; Ward, Rabab K
Reducing the radiation dose in computed tomography (CT) is highly desirable but it leads to excessive noise in the projection measurements. This can significantly reduce the diagnostic value of the reconstructed images. Removing the noise in the projection measurements is, therefore, essential for reconstructing high-quality images, especially in low-dose CT. In recent years, two new classes of patch-based denoising algorithms proved superior to other methods in various denoising applications. The first class is based on sparse representation of image patches in a learned dictionary. The second class is based on the non-local means method. Here, the image is searched for similar patches and the patches are processed together to find their denoised estimates. In this paper, we propose a novel denoising algorithm for cone-beam CT projections. The proposed method has similarities to both these algorithmic classes but is more effective and much faster. In order to exploit both the correlation between neighboring pixels within a projection and the correlation between pixels in neighboring projections, the proposed algorithm stacks noisy cone-beam projections together to form a 3D image and extracts small overlapping 3D blocks from this 3D image for processing. We propose a fast algorithm for clustering all extracted blocks. The central assumption in the proposed algorithm is that all blocks in a cluster have a joint-sparse representation in a well-designed dictionary. We describe algorithms for learning such a dictionary and for denoising a set of projections using this dictionary. We apply the proposed algorithm on simulated and real data and compare it with three other algorithms. Our results show that the proposed algorithm outperforms some of the best denoising algorithms, while also being much faster. (paper)
Time-Frequency Distribution of Music based on Sparse Wavelet Packet Representations
Endelt, Line Ørtoft
We introduce a new method for generating time-frequency distributions, which is particularly useful for the analysis of music signals. The method presented here is based on $\\ell1$ sparse representations of music signals in a redundant wavelet packet dictionary. The representations are found using...... the minimization methods basis pursuit and best orthogonal basis. Visualizations of the time-frequency distribution are constructed based on a simplified energy distribution in the wavelet packet decomposition. The time-frequency distributions emphasizes structured musical content, including non-stationary content...
Sparse filtering with the generalized lp/lq norm and its applications to the condition monitoring of rotating machinery
Jia, Xiaodong; Zhao, Ming; Di, Yuan; Li, Pin; Lee, Jay
Sparsity is becoming a more and more important topic in the area of machine learning and signal processing recently. One big family of sparse measures in current literature is the generalized lp /lq norm, which is scale invariant and is widely regarded as normalized lp norm. However, the characteristics of the generalized lp /lq norm are still less discussed and its application to the condition monitoring of rotating devices has been still unexplored. In this study, we firstly discuss the characteristics of the generalized lp /lq norm for sparse optimization and then propose a method of sparse filtering with the generalized lp /lq norm for the purpose of impulsive signature enhancement. Further driven by the trend of industrial big data and the need of reducing maintenance cost for industrial equipment, the proposed sparse filter is customized for vibration signal processing and also implemented on bearing and gearbox for the purpose of condition monitoring. Based on the results from the industrial implementations in this paper, the proposed method has been found to be a promising tool for impulsive feature enhancement, and the superiority of the proposed method over previous methods is also demonstrated.
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Wang, J.J.-Y.
Impulse noise estimation and removal for OFDM systems
Al-Naffouri, Tareq Y.
Orthogonal Frequency Division Multiplexing (OFDM) is a modulation scheme that is widely used in wired and wireless communication systems. While OFDM is ideally suited to deal with frequency selective channels and AWGN, its performance may be dramatically impacted by the presence of impulse noise. In fact, very strong noise impulses in the time domain might result in the erasure of whole OFDM blocks of symbols at the receiver. Impulse noise can be mitigated by considering it as a sparse signal in time, and using recently developed algorithms for sparse signal reconstruction. We propose an algorithm that utilizes the guard band subcarriers for the impulse noise estimation and cancellation. Instead of relying on ℓ1 minimization as done in some popular general-purpose compressive sensing schemes, the proposed method jointly exploits the specific structure of this problem and the available a priori information for sparse signal recovery. The computational complexity of the proposed algorithm is very competitive with respect to sparse signal reconstruction schemes based on ℓ1 minimization. The proposed method is compared with respect to other state-of-the-art methods in terms of achievable rates for an OFDM system with impulse noise and AWGN. © 2014 IEEE.
Al-Naffouri, Tareq Y.; Quadeer, Ahmed Abdul; Caire, Giuseppe
Volumetric CT with sparse detector arrays (and application to Si-strip photon counters).
Sisniega, A; Zbijewski, W; Stayman, J W; Xu, J; Taguchi, K; Fredenberg, E; Lundqvist, Mats; Siewerdsen, J H
Novel x-ray medical imaging sensors, such as photon counting detectors (PCDs) and large area CCD and CMOS cameras can involve irregular and/or sparse sampling of the detector plane. Application of such detectors to CT involves undersampling that is markedly different from the commonly considered case of sparse angular sampling. This work investigates volumetric sampling in CT systems incorporating sparsely sampled detectors with axial and helical scan orbits and evaluates performance of model-based image reconstruction (MBIR) with spatially varying regularization in mitigating artifacts due to sparse detector sampling. Volumetric metrics of sampling density and uniformity were introduced. Penalized-likelihood MBIR with a spatially varying penalty that homogenized resolution by accounting for variations in local sampling density (i.e. detector gaps) was evaluated. The proposed methodology was tested in simulations and on an imaging bench based on a Si-strip PCD (total area 5 cm  ×  25 cm) consisting of an arrangement of line sensors separated by gaps of up to 2.5 mm. The bench was equipped with translation/rotation stages allowing a variety of scanning trajectories, ranging from a simple axial acquisition to helical scans with variable pitch. Statistical (spherical clutter) and anthropomorphic (hand) phantoms were considered. Image quality was compared to that obtained with a conventional uniform penalty in terms of structural similarity index (SSIM), image uniformity, spatial resolution, contrast, and noise. Scan trajectories with intermediate helical width (~10 mm longitudinal distance per 360° rotation) demonstrated optimal tradeoff between the average sampling density and the homogeneity of sampling throughout the volume. For a scan trajectory with 10.8 mm helical width, the spatially varying penalty resulted in significant visual reduction of sampling artifacts, confirmed by a 10% reduction in minimum SSIM (from 0.88 to 0.8) and a 40
Transcranial passive acoustic mapping with hemispherical sparse arrays using CT-based skull-specific aberration corrections: a simulation study
Jones, Ryan M; O'Reilly, Meaghan A; Hynynen, Kullervo
The feasibility of transcranial passive acoustic mapping with hemispherical sparse arrays (30 cm diameter, 16 to 1372 elements, 2.48 mm receiver diameter) using CT-based aberration corrections was investigated via numerical simulations. A multi-layered ray acoustic transcranial ultrasound propagation model based on CT-derived skull morphology was developed. By incorporating skull-specific aberration corrections into a conventional passive beamforming algorithm (Norton and Won 2000 IEEE Trans. Geosci. Remote Sens. 38 1337–43), simulated acoustic source fields representing the emissions from acoustically-stimulated microbubbles were spatially mapped through three digitized human skulls, with the transskull reconstructions closely matching the water-path control images. Image quality was quantified based on main lobe beamwidths, peak sidelobe ratio, and image signal-to-noise ratio. The effects on the resulting image quality of the source's emission frequency and location within the skull cavity, the array sparsity and element configuration, the receiver element sensitivity, and the specific skull morphology were all investigated. The system's resolution capabilities were also estimated for various degrees of array sparsity. Passive imaging of acoustic sources through an intact skull was shown possible with sparse hemispherical imaging arrays. This technique may be useful for the monitoring and control of transcranial focused ultrasound (FUS) treatments, particularly non-thermal, cavitation-mediated applications such as FUS-induced blood–brain barrier disruption or sonothrombolysis, for which no real-time monitoring techniques currently exist. (paper)
Jones, Ryan M.; O'Reilly, Meaghan A.; Hynynen, Kullervo
The feasibility of transcranial passive acoustic mapping with hemispherical sparse arrays (30 cm diameter, 16 to 1372 elements, 2.48 mm receiver diameter) using CT-based aberration corrections was investigated via numerical simulations. A multi-layered ray acoustic transcranial ultrasound propagation model based on CT-derived skull morphology was developed. By incorporating skull-specific aberration corrections into a conventional passive beamforming algorithm (Norton and Won 2000 IEEE Trans. Geosci. Remote Sens. 38 1337–43), simulated acoustic source fields representing the emissions from acoustically-stimulated microbubbles were spatially mapped through three digitized human skulls, with the transskull reconstructions closely matching the water-path control images. Image quality was quantified based on main lobe beamwidths, peak sidelobe ratio, and image signal-to-noise ratio. The effects on the resulting image quality of the source's emission frequency and location within the skull cavity, the array sparsity and element configuration, the receiver element sensitivity, and the specific skull morphology were all investigated. The system's resolution capabilities were also estimated for various degrees of array sparsity. Passive imaging of acoustic sources through an intact skull was shown possible with sparse hemispherical imaging arrays. This technique may be useful for the monitoring and control of transcranial focused ultrasound (FUS) treatments, particularly non-thermal, cavitation-mediated applications such as FUS-induced blood-brain barrier disruption or sonothrombolysis, for which no real-time monitoring technique currently exists. PMID:23807573
Sparse Regression by Projection and Sparse Discriminant Analysis
Qi, Xin
© 2015, © American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high-dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross-validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares, and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared with the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplementary materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.
Sparse distributed memory overview
Raugh, Mike
The Sparse Distributed Memory (SDM) project is investigating the theory and applications of massively parallel computing architecture, called sparse distributed memory, that will support the storage and retrieval of sensory and motor patterns characteristic of autonomous systems. The immediate objectives of the project are centered in studies of the memory itself and in the use of the memory to solve problems in speech, vision, and robotics. Investigation of methods for encoding sensory data is an important part of the research. Examples of NASA missions that may benefit from this work are Space Station, planetary rovers, and solar exploration. Sparse distributed memory offers promising technology for systems that must learn through experience and be capable of adapting to new circumstances, and for operating any large complex system requiring automatic monitoring and control. Sparse distributed memory is a massively parallel architecture motivated by efforts to understand how the human brain works. Sparse distributed memory is an associative memory, able to retrieve information from cues that only partially match patterns stored in the memory. It is able to store long temporal sequences derived from the behavior of a complex system, such as progressive records of the system's sensory data and correlated records of the system's motor controls.
Senkin Sergey
Full Text Available The ATLAS Collaboration has started a vast programme of upgrades in the context of high-luminosity LHC (HL-LHC foreseen in 2024. We present here one of the frontend readout options, an ASIC called FATALIC, proposed for the high-luminosity phase LHC upgrade of the ATLAS Tile Calorimeter. Based on a 130 nm CMOS technology, FATALIC performs the complete signal processing, including amplification, shaping and digitisation. We describe the full characterisation of FATALIC and also the Optimal Filtering signal reconstruction method adapted to fully exploit the FATALIC three-range layout. Additionally we present the resolution performance of the whole chain measured using the charge injection system designed for calibration. Finally we discuss the results of the signal reconstruction used on real data collected during a preliminary beam test at CERN.
Senkin, Sergey
The ATLAS Collaboration has started a vast programme of upgrades in the context of high-luminosity LHC (HL-LHC) foreseen in 2024. We present here one of the frontend readout options, an ASIC called FATALIC, proposed for the high-luminosity phase LHC upgrade of the ATLAS Tile Calorimeter. Based on a 130 nm CMOS technology, FATALIC performs the complete signal processing, including amplification, shaping and digitisation. We describe the full characterisation of FATALIC and also the Optimal Filtering signal reconstruction method adapted to fully exploit the FATALIC three-range layout. Additionally we present the resolution performance of the whole chain measured using the charge injection system designed for calibration. Finally we discuss the results of the signal reconstruction used on real data collected during a preliminary beam test at CERN.
In-place sparse suffix sorting
Prezza, Nicola
information regarding the lexicographical order of a size-b subset of all n text suffixes is often needed. Such information can be stored space-efficiently (in b words) in the sparse suffix array (SSA). The SSA and its relative sparse LCP array (SLCP) can be used as a space-efficient substitute of the sparse...... suffix tree. Very recently, Gawrychowski and Kociumaka [11] showed that the sparse suffix tree (and therefore SSA and SLCP) can be built in asymptotically optimal O(b) space with a Monte Carlo algorithm running in O(n) time. The main reason for using the SSA and SLCP arrays in place of the sparse suffix...... tree is, however, their reduced space of b words each. This leads naturally to the quest for in-place algorithms building these arrays. Franceschini and Muthukrishnan [8] showed that the full suffix array can be built in-place and in optimal running time. On the other hand, finding sub-quadratic in...
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Branicki, M.; Majda, A.J.
of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models
Self-expressive Dictionary Learning for Dynamic 3D Reconstruction.
Zheng, Enliang; Ji, Dinghuang; Dunn, Enrique; Frahm, Jan-Michael
We target the problem of sparse 3D reconstruction of dynamic objects observed by multiple unsynchronized video cameras with unknown temporal overlap. To this end, we develop a framework to recover the unknown structure without sequencing information across video sequences. Our proposed compressed sensing framework poses the estimation of 3D structure as the problem of dictionary learning, where the dictionary is defined as an aggregation of the temporally varying 3D structures. Given the smooth motion of dynamic objects, we observe any element in the dictionary can be well approximated by a sparse linear combination of other elements in the same dictionary (i.e. self-expression). Our formulation optimizes a biconvex cost function that leverages a compressed sensing formulation and enforces both structural dependency coherence across video streams, as well as motion smoothness across estimates from common video sources. We further analyze the reconstructability of our approach under different capture scenarios, and its comparison and relation to existing methods. Experimental results on large amounts of synthetic data as well as real imagery demonstrate the effectiveness of our approach.
Measuring displacement signal with an accelerometer
Han, Sang Bo
An effective and simple way to reconstruct displacement signal from a measured acceleration signal is proposed in this paper. To reconstruct displacement signal by means of double-integrating the time domain acceleration signal, the Nyquist frequency of the digital sampling of the acceleration signal should be much higher than the highest frequency component of the signal. On the other hand, to reconstruct displacement signal by taking the inverse Fourier transform, the magnitude of the significant frequency components of the Fourier transform of the acceleration signal should be greater than the 6 dB increment line along the frequency axis. With a predetermined resolution in time and frequency domain, determined by the sampling rate to measure and record the original signal, reconstructing high-frequency signals in the time domain and reconstructing low-frequency signals in the frequency domain will produce biased errors. Furthermore, because of the DC components inevitably included in the sampling process, low-frequency components of the signals are overestimated when displacement signals are reconstructed from the Fourier transform of the acceleration signal. The proposed method utilizes curve-fitting around the significant frequency components of the Fourier transform of the acceleration signal before it is inverse-Fourier transformed. Curve-fitting around the dominant frequency components provides much better results than simply ignoring the insignificant frequency components of the signal
Classification of multispectral or hyperspectral satellite imagery using clustering of sparse approximations on sparse representations in learned dictionaries obtained using efficient convolutional sparse coding
Moody, Daniela; Wohlberg, Brendt
An approach for land cover classification, seasonal and yearly change detection and monitoring, and identification of changes in man-made features may use a clustering of sparse approximations (CoSA) on sparse representations in learned dictionaries. The learned dictionaries may be derived using efficient convolutional sparse coding to build multispectral or hyperspectral, multiresolution dictionaries that are adapted to regional satellite image data. Sparse image representations of images over the learned dictionaries may be used to perform unsupervised k-means clustering into land cover categories. The clustering process behaves as a classifier in detecting real variability. This approach may combine spectral and spatial textural characteristics to detect geologic, vegetative, hydrologic, and man-made features, as well as changes in these features over time.
SAR and Infrared Image Fusion in Complex Contourlet Domain Based on Joint Sparse Representation
Wu Yiquan
Full Text Available To investigate the problems of the large grayscale difference between infrared and Synthetic Aperture Radar (SAR images and their fusion image not being fit for human visual perception, we propose a fusion method for SAR and infrared images in the complex contourlet domain based on joint sparse representation. First, we perform complex contourlet decomposition of the infrared and SAR images. Then, we employ the KSingular Value Decomposition (K-SVD method to obtain an over-complete dictionary of the low-frequency components of the two source images. Using a joint sparse representation model, we then generate a joint dictionary. We obtain the sparse representation coefficients of the low-frequency components of the source images in the joint dictionary by the Orthogonal Matching Pursuit (OMP method and select them using the selection maximization strategy. We then reconstruct these components to obtain the fused low-frequency components and fuse the high-frequency components using two criteria——the coefficient of visual sensitivity and the degree of energy matching. Finally, we obtain the fusion image by the inverse complex contourlet transform. Compared with the three classical fusion methods and recently presented fusion methods, e.g., that based on the Non-Subsampled Contourlet Transform (NSCT and another based on sparse representation, the method we propose in this paper can effectively highlight the salient features of the two source images and inherit their information to the greatest extent.
Discrete Sparse Coding.
Exarchakis, Georgios; Lücke, Jörg
Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1)Â we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2)Â use image patches of natural images and discuss the role of the prior for the extraction of image components, (3)Â use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.
Sparsity reconstruction in electrical impedance tomography: An experimental evaluation
Gehre, Matthias
We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ℓ1-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ℓ1-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. © 2011 Elsevier B.V. All rights reserved.
Sensing RF signals with the optical wideband converter
Valley, George C.; Sefler, George A.; Shaw, T. J.
The optical wideband converter (OWC) is a system for measuring properties of RF signals in the GHz band without use of high speed electronics. In the OWC the RF signal is modulated on a repetitively pulsed optical field with a large wavelength chirp, the optical field is diffracted onto a spatial light modulator (SLM) whose pixels are modulated with a pseudo-random bit sequences (PRBSs), and finally the optical field is directed to a photodiode and the resulting current integrated for each PRBS. When the number of PRBSs and measurements equals the number of SLM pixels, the RF signal can be obtained in principle by multiplying the measurement vector by the inverse of the square matrix given by the PRBSs and the properties of the optics. When the number of measurements is smaller than the number of pixels, a compressive sensing (CS) measurement can be performed, and sparse RF signals can be obtained using one of the standard CS recovery algorithms such as the penalized l1 norm (also known as basis pursuit) or one of the variants of matching pursuit. Accurate reconstruction of RF signals requires good calibration of the OWC. In this paper, we present results using the OWC for RF signals consisting of 2 sinusoids recovered using 3 techniques (matrix inversion, basis pursuit, and matching pursuit). We compare results obtained with orthogonal matching pursuit with nonlinear least squares to basis pursuit with an over-complete dictionary.
Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation
Takeda, Koujin; Kabashima, Yoshiyuki
We propose a systematic method for constructing a sparse data reconstruction algorithm in compressed sensing at a relatively low computational cost for general observation matrix. It is known that the cost of â"" 1 -norm minimization using a standard linear programming algorithm is O(N 3 ). We show that this cost can be reduced to O(N 2 ) by applying the approach of posterior maximization. Furthermore, in principle, the algorithm from our approach is expected to achieve the widest successful reconstruction region, which is evaluated from theoretical argument. We also discuss the relation between the belief propagation-based reconstruction algorithm introduced in preceding works and our approach
Statistical selection of tide gauges for Arctic sea-level reconstruction
Svendsen, Peter Limkilde; Andersen, Ole Baltazar; Nielsen, Allan Aasbjerg
In this paper, we seek an appropriate selection of tide gauges for Arctic Ocean sea-level reconstruction based on a combination of empirical criteria and statistical properties (leverages). Tide gauges provide the only in situ observations of sea level prior to the altimetry era. However, tide...... the "influence" of each Arctic tide gauge on the EOF-based reconstruction through the use of statistical leverage and use this as an indication in selecting appropriate tide gauges, in order to procedurally identify poor-quality data while still including as much data as possible. To accommodate sparse...
lpNet: a linear programming approach to reconstruct signal transduction networks.
Matos, Marta R A; Knapp, Bettina; Kaderali, Lars
With the widespread availability of high-throughput experimental technologies it has become possible to study hundreds to thousands of cellular factors simultaneously, such as coding- or non-coding mRNA or protein concentrations. Still, extracting information about the underlying regulatory or signaling interactions from these data remains a difficult challenge. We present a flexible approach towards network inference based on linear programming. Our method reconstructs the interactions of factors from a combination of perturbation/non-perturbation and steady-state/time-series data. We show both on simulated and real data that our methods are able to reconstruct the underlying networks fast and efficiently, thus shedding new light on biological processes and, in particular, into disease's mechanisms of action. We have implemented the approach as an R package available through bioconductor. This R package is freely available under the Gnu Public License (GPL-3) from bioconductor.org (http://bioconductor.org/packages/release/bioc/html/lpNet.html) and is compatible with most operating systems (Windows, Linux, Mac OS) and hardware architectures. bettina.knapp@helmholtz-muenchen.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy
Marandi, Ahmadreza; de Klerk, Etienne; Dahl, Joachim
The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal
Robust and Secure Watermarking Using Sparse Information of Watermark for Biometric Data Protection
Rohit M Thanki
Full Text Available Biometric based human authentication system is used for security purpose in many organizations in the present world. This biometric authentication system has several vulnerable points. Two of vulnerable points are protection of biometric templates at system database and protection of biometric templates at communication channel between two modules of biometric authentication systems. In this paper proposed a robust watermarking scheme using the sparse information of watermark biometric to secure vulnerable point like protection of biometric templates at the communication channel of biometric authentication systems. A compressive sensing theory procedure is used for generation of sparse information on watermark biometric data using detail wavelet coefficients. Then sparse information of watermark biometric data is embedded into DCT coefficients of host biometric data. This proposed scheme is robust to common signal processing and geometric attacks like JPEG compression, adding noise, filtering, and cropping, histogram equalization. This proposed scheme has more advantages and high quality measures compared to existing schemes in the literature.
Fast Algorithms for High-Order Sparse Linear Prediction with Applications to Speech Processing
Jensen, Tobias Lindstrøm; Giacobello, Daniele; van Waterschoot, Toon
In speech processing applications, imposing sparsity constraints on high-order linear prediction coefficients and prediction residuals has proven successful in overcoming some of the limitation of conventional linear predictive modeling. However, this modeling scheme, named sparse linear prediction...... problem with lower accuracy than in previous work. In the experimental analysis, we clearly show that a solution with lower accuracy can achieve approximately the same performance as a high accuracy solution both objectively, in terms of prediction gain, as well as with perceptual relevant measures, when...... evaluated in a speech reconstruction application....
Sparse estimation of model-based diffuse thermal dust emission
Irfan, Melis O.; Bobin, Jérôme
Component separation for the Planck High Frequency Instrument (HFI) data is primarily concerned with the estimation of thermal dust emission, which requires the separation of thermal dust from the cosmic infrared background (CIB). For that purpose, current estimation methods rely on filtering techniques to decouple thermal dust emission from CIB anisotropies, which tend to yield a smooth, low-resolution, estimation of the dust emission. In this paper, we present a new parameter estimation method, premise: Parameter Recovery Exploiting Model Informed Sparse Estimates. This method exploits the sparse nature of thermal dust emission to calculate all-sky maps of thermal dust temperature, spectral index, and optical depth at 353 GHz. premise is evaluated and validated on full-sky simulated data. We find the percentage difference between the premise results and the true values to be 2.8, 5.7, and 7.2 per cent at the 1σ level across the full sky for thermal dust temperature, spectral index, and optical depth at 353 GHz, respectively. A comparison between premise and a GNILC-like method over selected regions of our sky simulation reveals that both methods perform comparably within high signal-to-noise regions. However, outside of the Galactic plane, premise is seen to outperform the GNILC-like method with increasing success as the signal-to-noise ratio worsens.
Sparse inverse covariance estimation with the graphical lasso.
Friedman, Jerome; Hastie, Trevor; Tibshirani, Robert
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm--the graphical lasso--that is remarkably fast: It solves a 1000-node problem ( approximately 500,000 parameters) in at most a minute and is 30-4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
Wind Noise Reduction using Non-negative Sparse Coding
Schmidt, Mikkel N.; Larsen, Jan; Hsiao, Fu-Tien
We introduce a new speaker independent method for reducing wind noise in single-channel recordings of noisy speech. The method is based on non-negative sparse coding and relies on a wind noise dictionary which is estimated from an isolated noise recording. We estimate the parameters of the model ...... and discuss their sensitivity. We then compare the algorithm with the classical spectral subtraction method and the Qualcomm-ICSI-OGI noise reduction method. We optimize the sound quality in terms of signal-to-noise ratio and provide results on a noisy speech recognition task....
Sparse PCA, a new method for unsupervised analyses of fMRI data
Sjöstrand, Karl; Lund, Torben E.; Madsen, Kristoffer Hougaard
favorable circumstances, one of more of these signals describe activation patterns, while others model noise and other nuisance factors. This work introduces a competing method for fMRI analysis known as sparse principal component analysis (SPCA). We argue that SPCA is less committed than ICA and show...... that similar results, with better suppression of noise, are obtained....
Limited angle CT reconstruction by simultaneous spatial and Radon domain regularization based on TV and data-driven tight frame
Zhang, Wenkun; Zhang, Hanming; Wang, Linyuan; Cai, Ailong; Li, Lei; Yan, Bin
Limited angle computed tomography (CT) reconstruction is widely performed in medical diagnosis and industrial testing because of the size of objects, engine/armor inspection requirements, and limited scan flexibility. Limited angle reconstruction necessitates usage of optimization-based methods that utilize additional sparse priors. However, most of conventional methods solely exploit sparsity priors of spatial domains. When CT projection suffers from serious data deficiency or various noises, obtaining reconstruction images that meet the requirement of quality becomes difficult and challenging. To solve this problem, this paper developed an adaptive reconstruction method for limited angle CT problem. The proposed method simultaneously uses spatial and Radon domain regularization model based on total variation (TV) and data-driven tight frame. Data-driven tight frame being derived from wavelet transformation aims at exploiting sparsity priors of sinogram in Radon domain. Unlike existing works that utilize pre-constructed sparse transformation, the framelets of the data-driven regularization model can be adaptively learned from the latest projection data in the process of iterative reconstruction to provide optimal sparse approximations for given sinogram. At the same time, an effective alternating direction method is designed to solve the simultaneous spatial and Radon domain regularization model. The experiments for both simulation and real data demonstrate that the proposed algorithm shows better performance in artifacts depression and details preservation than the algorithms solely using regularization model of spatial domain. Quantitative evaluations for the results also indicate that the proposed algorithm applying learning strategy performs better than the dual domains algorithms without learning regularization model
Sparse and Adaptive Diffusion Dictionary (SADD) for recovering intra-voxel white matter structure.
Aranda, Ramon; Ramirez-Manzanares, Alonso; Rivera, Mariano
On the analysis of the Diffusion-Weighted Magnetic Resonance Images, multi-compartment models overcome the limitations of the well-known Diffusion Tensor model for fitting in vivo brain axonal orientations at voxels with fiber crossings, branching, kissing or bifurcations. Some successful multi-compartment methods are based on diffusion dictionaries. The diffusion dictionary-based methods assume that the observed Magnetic Resonance signal at each voxel is a linear combination of the fixed dictionary elements (dictionary atoms). The atoms are fixed along different orientations and diffusivity profiles. In this work, we present a sparse and adaptive diffusion dictionary method based on the Diffusion Basis Functions Model to estimate in vivo brain axonal fiber populations. Our proposal overcomes the following limitations of the diffusion dictionary-based methods: the limited angular resolution and the fixed shapes for the atom set. We propose to iteratively re-estimate the orientations and the diffusivity profile of the atoms independently at each voxel by using a simplified and easier-to-solve mathematical approach. As a result, we improve the fitting of the Diffusion-Weighted Magnetic Resonance signal. The advantages with respect to the former Diffusion Basis Functions method are demonstrated on the synthetic data-set used on the 2012 HARDI Reconstruction Challenge and in vivo human data. We demonstrate that improvements obtained in the intra-voxel fiber structure estimations benefit brain research allowing to obtain better tractography estimations. Hence, these improvements result in an accurate computation of the brain connectivity patterns. Copyright © 2015 Elsevier B.V. All rights reserved.
A novel integrated circuit for semiconductor radiation detectors with sparse readout
Zhang Yacong; Chen Zhognjian; Lu Wengao; Zhao Baoying; Ji Lijiu
A novel fully integrated CMOS readout circuit for semiconductor radiation detector with sparse readout is presented. The new sparse scheme is: when one channel is being read out, the trigger signal from other channels is delayed and then processed. Therefore, the dead time is reduced and so is the error rate. Besides sparse readout, sequential readout is also allowed, which means the analog voltages and addresses of all the channels are read out sequentially once there is a channel triggered. The circuit comprises Charge Sensitive Amplifier (CSA), pulse shaper, peak detect and hold circuit, and digital logic. A test chip of four channels designed in a 0.5 μ DPTM CMOS technology has been taped out. The results of post simulation indicate that the gain is 79.3 mV/fC with a linearity of 99.92%. The power dissipation is 4 mW per channel. Theory analysis and calculation shows that the error probability is approximately 2.5%, which means a reduction of about 37% is obtained compared with the traditional scanning scheme, assuming a 16-channel system with a particle rate of 100 k/s per channel. (authors)
Low order anti-aliasing filters for sparse signals in embedded ...
Indian Academy of Sciences (India)
The computation load increases only linearly with the number of signals, N since the ... We have considered, for simulation, the simple case of acquiring two signals .... Oppenheim A V and Schafer R W 1989 Discrete-time signal processing.
Aspect-Aided Dynamic Non-Negative Sparse Representation-Based Microwave Image Classification
Xinzheng Zhang
Full Text Available Classification of target microwave images is an important application in much areas such as security, surveillance, etc. With respect to the task of microwave image classification, a recognition algorithm based on aspect-aided dynamic non-negative least square (ADNNLS sparse representation is proposed. Firstly, an aspect sector is determined, the center of which is the estimated aspect angle of the testing sample. The training samples in the aspect sector are divided into active atoms and inactive atoms by smooth self-representative learning. Secondly, for each testing sample, the corresponding active atoms are selected dynamically, thereby establishing dynamic dictionary. Thirdly, the testing sample is represented with â"" 1 -regularized non-negative sparse representation under the corresponding dynamic dictionary. Finally, the class label of the testing sample is identified by use of the minimum reconstruction error. Verification of the proposed algorithm was conducted using the Moving and Stationary Target Acquisition and Recognition (MSTAR database which was acquired by synthetic aperture radar. Experiment results validated that the proposed approach was able to capture the local aspect characteristics of microwave images effectively, thereby improving the classification performance.
Qi, Xin; Luo, Ruiyan; Carroll, Raymond J.; Zhao, Hongyu
predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths
Iatrogenic Pneumothorax as a Complication to Delayed Breast Reconstruction With Tissue Expander—A Case Report
Willert, Cecilie Balslev; Bredgaard, Rikke
Breast reconstruction with expander implant is the most common breast reconstructive procedure. Irradiated patients are seldom reconstructed this way because the tissue expansion is difficult and the complication rates are higher. Pneumothorax is a serious condition and can be seen as a complicat......Breast reconstruction with expander implant is the most common breast reconstructive procedure. Irradiated patients are seldom reconstructed this way because the tissue expansion is difficult and the complication rates are higher. Pneumothorax is a serious condition and can be seen...... as a complication to the operation. Literature is sparse; hence, the only study is by Schneider et al who found an incidence of 0.55%. The study focused on immediate reconstruction only and did not report the percentage of irradiated patients. We present a unique case of iatrogenic pneumothorax in a previously...
Duality reconstruction algorithm for use in electrical impedance tomography
Abdullah, M.Z.; Dickin, F.J.
A duality reconstruction algorithm for solving the inverse problem in electrical impedance tomography (EIT) is described. In this method, an algorithm based on the Geselowitz compensation (GC) theorem is used first to reconstruct an approximate version of the image. It is then fed as a first guessed data to the modified Newton-Raphson (MNR) algorithm which iteratively correct the image until a final acceptable solution is reached. The implementation of the GC and MNR based algorithms using the finite element method will be discussed. Reconstructed images produced by the algorithm will also be presented. Consideration is also given to the most computationally intensive aspects of the algorithm, namely the inversion of the large and sparse matrices. The methods taken to approximately compute the inverse ot those matrices will be outlined. (author)
Sparse-sampling with time-encoded (TICO) stimulated Raman scattering for fast image acquisition
Hakert, Hubertus; Eibl, Matthias; Karpf, Sebastian; Huber, Robert
Modern biomedical imaging modalities aim to provide researchers a multimodal contrast for a deeper insight into a specimen under investigation. A very promising technique is stimulated Raman scattering (SRS) microscopy, which can unveil the chemical composition of a sample with a very high specificity. Although the signal intensities are enhanced manifold to achieve a faster acquisition of images if compared to standard Raman microscopy, there is a trade-off between specificity and acquisition speed. Commonly used SRS concepts either probe only very few Raman transitions as the tuning of the applied laser sources is complicated or record whole spectra with a spectrometer based setup. While the first approach is fast, it reduces the specificity and the spectrometer approach records whole spectra -with energy differences where no Raman information is present-, which limits the acquisition speed. Therefore, we present a new approach based on the TICO-Raman concept, which we call sparse-sampling. The TICO-sparse-sampling setup is fully electronically controllable and allows probing of only the characteristic peaks of a Raman spectrum instead of always acquiring a whole spectrum. By reducing the spectral points to the relevant peaks, the acquisition time can be greatly reduced compared to a uniformly, equidistantly sampled Raman spectrum while the specificity and the signal to noise ratio (SNR) are maintained. Furthermore, all laser sources are completely fiber based. The synchronized detection enables a full resolution of the Raman signal, whereas the analogue and digital balancing allows shot noise limited detection. First imaging results with polystyrene (PS) and polymethylmethacrylate (PMMA) beads confirm the advantages of TICO sparse-sampling. We achieved a pixel dwell time as low as 35 μs for an image differentiating both species. The mechanical properties of the applied voice coil stage for scanning the sample currently limits even faster acquisition.
Visual recognition and inference using dynamic overcomplete sparse learning.
Murray, Joseph F; Kreutz-Delgado, Kenneth
We present a hierarchical architecture and learning algorithm for visual recognition and other visual inference tasks such as imagination, reconstruction of occluded images, and expectation-driven segmentation. Using properties of biological vision for guidance, we posit a stochastic generative world model and from it develop a simplified world model (SWM) based on a tractable variational approximation that is designed to enforce sparse coding. Recent developments in computational methods for learning overcomplete representations (Lewicki & Sejnowski, 2000; Teh, Welling, Osindero, & Hinton, 2003) suggest that overcompleteness can be useful for visual tasks, and we use an overcomplete dictionary learning algorithm (Kreutz-Delgado, et al., 2003) as a preprocessing stage to produce accurate, sparse codings of images. Inference is performed by constructing a dynamic multilayer network with feedforward, feedback, and lateral connections, which is trained to approximate the SWM. Learning is done with a variant of the back-propagation-through-time algorithm, which encourages convergence to desired states within a fixed number of iterations. Vision tasks require large networks, and to make learning efficient, we take advantage of the sparsity of each layer to update only a small subset of elements in a large weight matrix at each iteration. Experiments on a set of rotated objects demonstrate various types of visual inference and show that increasing the degree of overcompleteness improves recognition performance in difficult scenes with occluded objects in clutter.
Sparse representation based image interpolation with nonlocal autoregressive modeling.
Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.
Sparse decompositions in 'incoherent' dictionaries
Gribonval, R.; Nielsen, Morten
a unique sparse representation in such a dictionary. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of a combinatorial optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may...
Optimization-based reconstruction for reduction of CBCT artifact in IGRT
Xia, Dan; Zhang, Zheng; Paysan, Pascal; Seghers, Dieter; Brehm, Marcus; Munro, Peter; Sidky, Emil Y.; Pelizzari, Charles; Pan, Xiaochuan
Kilo-voltage cone-beam computed tomography (CBCT) plays an important role in image guided radiation therapy (IGRT) by providing 3D spatial information of tumor potentially useful for optimizing treatment planning. In current IGRT CBCT system, reconstructed images obtained with analytic algorithms, such as FDK algorithm and its variants, may contain artifacts. In an attempt to compensate for the artifacts, we investigate optimization-based reconstruction algorithms such as the ASD-POCS algorithm for potentially reducing arti- facts in IGRT CBCT images. In this study, using data acquired with a physical phantom and a patient subject, we demonstrate that the ASD-POCS reconstruction can significantly reduce artifacts observed in clinical re- constructions. Moreover, patient images reconstructed by use of the ASD-POCS algorithm indicate a contrast level of soft-tissue improved over that of the clinical reconstruction. We have also performed reconstructions from sparse-view data, and observe that, for current clinical imaging conditions, ASD-POCS reconstructions from data collected at one half of the current clinical projection views appear to show image quality, in terms of spatial and soft-tissue-contrast resolution, higher than that of the corresponding clinical reconstructions.
Sparse aperture differential piston measurements using the pyramid wave-front sensor
Arcidiacono, Carmelo; Chen, Xinyang; Yan, Zhaojun; Zheng, Lixin; Agapito, Guido; Wang, Chaoyan; Zhu, Nenghong; Zhu, Liyun; Cai, Jianqing; Tang, Zhenghong
In this paper we report on the laboratory experiment we settled in the Shanghai Astronomical Observatory (SHAO) to investigate the pyramid wave-front sensor (WFS) ability to measure the differential piston on a sparse aperture. The ultimate goal is to verify the ability of the pyramid WFS work in close loop to perform the phasing of the primary mirrors of a sparse Fizeau imaging telescope. In the experiment we installed on the optical bench we performed various test checking the ability to flat the wave-front using a deformable mirror and to measure the signal of the differential piston on a two pupils setup. These steps represent the background from which we start to perform full close loop operation on multiple apertures. These steps were also useful to characterize the achromatic double pyramids (double prisms) manufactured in the SHAO optical workshop.
Proceedings of the third "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'16)
The third edition of the "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) took place in Aalborg, the 4th largest city in Denmark situated beautifully in the northern part of the country, from the 24th to 26th of August 2016. The workshop venue...... learning; Optimization for sparse modelling; Information theory, geometry and randomness; Sparsity? What's next? (Discrete-valued signals; Union of low-dimensional spaces, Cosparsity, mixed/group norm, model-based, low-complexity models, ...); Matrix/manifold sensing/processing (graph, low...
SVM-Based Spectral Analysis for Heart Rate from Multi-Channel WPPG Sensor Signals.
Xiong, Jiping; Cai, Lisang; Wang, Fei; He, Xiaowei
Although wrist-type photoplethysmographic (hereafter referred to as WPPG) sensor signals can measure heart rate quite conveniently, the subjects' hand movements can cause strong motion artifacts, and then the motion artifacts will heavily contaminate WPPG signals. Hence, it is challenging for us to accurately estimate heart rate from WPPG signals during intense physical activities. The WWPG method has attracted more attention thanks to the popularity of wrist-worn wearable devices. In this paper, a mixed approach called Mix-SVM is proposed, it can use multi-channel WPPG sensor signals and simultaneous acceleration signals to measurement heart rate. Firstly, we combine the principle component analysis and adaptive filter to remove a part of the motion artifacts. Due to the strong relativity between motion artifacts and acceleration signals, the further denoising problem is regarded as a sparse signals reconstruction problem. Then, we use a spectrum subtraction method to eliminate motion artifacts effectively. Finally, the spectral peak corresponding to heart rate is sought by an SVM-based spectral analysis method. Through the public PPG database in the 2015 IEEE Signal Processing Cup, we acquire the experimental results, i.e., the average absolute error was 1.01 beat per minute, and the Pearson correlation was 0.9972. These results also confirm that the proposed Mix-SVM approach has potential for multi-channel WPPG-based heart rate estimation in the presence of intense physical exercise.
Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition
Tang, Xin; Feng, Guo-can; Li, Xiao-xin; Cai, Jia-xin
Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the
Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition.
Xin Tang
Full Text Available Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC. Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our
Methods of X-ray CT image reconstruction from few projections
To improve the safety (low dose) and the productivity (fast acquisition) of a X-ray CT system, we want to reconstruct a high quality image from a small number of projections. The classical reconstruction algorithms generally fail since the reconstruction procedure is unstable and suffers from artifacts. A new approach based on the recently developed 'Compressed Sensing' (CS) theory assumes that the unknown image is in some sense 'sparse' or 'compressible', and the reconstruction is formulated through a non linear optimization problem (TV/l1 minimization) by enhancing the sparsity. Using the pixel (or voxel in 3D) as basis, to apply the CS framework in CT one usually needs a 'sparsifying' transform, and combines it with the 'X-ray projector' which applies on the pixel image. In this thesis, we have adapted a 'CT-friendly' radial basis of Gaussian family called 'blob' to the CS-CT framework. The blob has better space-frequency localization properties than the pixel, and many operations, such as the X-ray transform, can be evaluated analytically and are highly parallelizable (on GPU platform). Compared to the classical Kaisser-Bessel blob, the new basis has a multi-scale structure: an image is the sum of dilated and translated radial Mexican hat functions. The typical medical objects are compressible under this basis, so the sparse representation system used in the ordinary CS algorithms is no more needed. 2D simulations show that the existing TV and l1 algorithms are more efficient and the reconstructions have better visual quality than the equivalent approach based on the pixel or wavelet basis. The new approach has also been validated on 2D experimental data, where we have observed that in general the number of projections can be reduced to about 50%, without compromising the image quality. (author) [fr
Data analysis in high-dimensional sparse spaces
Clemmensen, Line Katrine Harder
classification techniques for high-dimensional problems are presented: Sparse discriminant analysis, sparse mixture discriminant analysis and orthogonality constrained support vector machines. The first two introduces sparseness to the well known linear and mixture discriminant analysis and thereby provide low...... are applied to classifications of fish species, ear canal impressions used in the hearing aid industry, microbiological fungi species, and various cancerous tissues and healthy tissues. In addition, novel applications of sparse regressions (also called the elastic net) to the medical, concrete, and food...
A sparse-grid isogeometric solver
Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90's in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
Beck, Joakim
Sparse Representation of Deformable 3D Organs with Spherical Harmonics and Structured Dictionary
Dan Wang
Full Text Available This paper proposed a novel algorithm to sparsely represent a deformable surface (SRDS with low dimensionality based on spherical harmonic decomposition (SHD and orthogonal subspace pursuit (OSP. The key idea in SRDS method is to identify the subspaces from a training data set in the transformed spherical harmonic domain and then cluster each deformation into the best-fit subspace for fast and accurate representation. This algorithm is also generalized into applications of organs with both interior and exterior surfaces. To test the feasibility, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques and then both ex vivo and in vivo experiments are conducted using 3D magnetic resonance imaging (MRI scans for verification in practical settings. All results demonstrated that the proposed algorithm features sparse representation of deformable surfaces with low dimensionality and high accuracy. Specifically, the precision evaluated as maximum error distance between the reconstructed surface and the MRI ground truth is better than 3 mm in real MRI experiments.
CARS Spectral Fitting with Multiple Resonant Species using Sparse Libraries
Cutler, Andrew D.; Magnotti, Gaetano
The dual pump CARS technique is often used in the study of turbulent flames. Fast and accurate algorithms are needed for fitting dual-pump CARS spectra for temperature and multiple chemical species. This paper describes the development of such an algorithm. The algorithm employs sparse libraries, whose size grows much more slowly with number of species than a conventional library. The method was demonstrated by fitting synthetic "experimental" spectra containing 4 resonant species (N2, O2, H2 and CO2), both with noise and without it, and by fitting experimental spectra from a H2-air flame produced by a Hencken burner. In both studies, weighted least squares fitting of signal, as opposed to least squares fitting signal or square-root signal, was shown to produce the least random error and minimize bias error in the fitted parameters.
Supervised Transfer Sparse Coding
Al-Shedivat, Maruan
A combination of the sparse coding and transfer learn- ing techniques was shown to be accurate and robust in classification tasks where training and testing objects have a shared feature space but are sampled from differ- ent underlying distributions, i.e., belong to different do- mains. The key assumption in such case is that in spite of the domain disparity, samples from different domains share some common hidden factors. Previous methods often assumed that all the objects in the target domain are unlabeled, and thus the training set solely comprised objects from the source domain. However, in real world applications, the target domain often has some labeled objects, or one can always manually label a small num- ber of them. In this paper, we explore such possibil- ity and show how a small number of labeled data in the target domain can significantly leverage classifica- tion accuracy of the state-of-the-art transfer sparse cod- ing methods. We further propose a unified framework named supervised transfer sparse coding (STSC) which simultaneously optimizes sparse representation, domain transfer and classification. Experimental results on three applications demonstrate that a little manual labeling and then learning the model in a supervised fashion can significantly improve classification accuracy.
Grey signal processing and data reconstruction in the non-diffracting beam triangulation measurement system
Meng, Hao; Wang, Zhongyu; Fu, Jihua
The non-diffracting beam triangulation measurement system possesses the advantages of longer measurement range, higher theoretical measurement accuracy and higher resolution over the traditional laser triangulation measurement system. Unfortunately the measurement accuracy of the system is greatly degraded due to the speckle noise, the CCD photoelectric noise and the background light noise in practical applications. Hence, some effective signal processing methods must be applied to improve the measurement accuracy. In this paper a novel effective method for removing the noises in the non-diffracting beam triangulation measurement system is proposed. In the method the grey system theory is used to process and reconstruct the measurement signal. Through implementing the grey dynamic filtering based on the dynamic GM(1,1), the noises can be effectively removed from the primary measurement data and the measurement accuracy of the system can be improved as a result.
Hybrid sparse blind deconvolution: an implementation of SOOT algorithm to real data
Pakmanesh, Parvaneh; Goudarzi, Alireza; Kourki, Meisam
Getting information of seismic data depends on deconvolution as an important processing step; it provides the reflectivity series by signal compression. This compression can be obtained by removing the wavelet effects on the traces. The recently blind deconvolution has provided reliable performance for sparse signal recovery. In this study, two deconvolution methods have been implemented to the seismic data; the convolution of these methods provides a robust spiking deconvolution approach. This hybrid deconvolution is applied using the sparse deconvolution (MM algorithm) and the Smoothed-One-Over-Two algorithm (SOOT) in a chain. The MM algorithm is based on the minimization of the cost function defined by standards l1 and l2. After applying the two algorithms to the seismic data, the SOOT algorithm provided well-compressed data with a higher resolution than the MM algorithm. The SOOT algorithm requires initial values to be applied for real data, such as the wavelet coefficients and reflectivity series that can be achieved through the MM algorithm. The computational cost of the hybrid method is high, and it is necessary to be implemented on post-stack or pre-stack seismic data of complex structure regions.
Sample size reduction in groundwater surveys via sparse data assimilation
Hussain, Z.; Muhammad, A.
In this paper, we focus on sparse signal recovery methods for data assimilation in groundwater models. The objective of this work is to exploit the commonly understood spatial sparsity in hydrodynamic models and thereby reduce the number of measurements to image a dynamic groundwater profile. To achieve this we employ a Bayesian compressive sensing framework that lets us adaptively select the next measurement to reduce the estimation error. An extension to the Bayesian compressive sensing framework is also proposed which incorporates the additional model information to estimate system states from even lesser measurements. Instead of using cumulative imaging-like measurements, such as those used in standard compressive sensing, we use sparse binary matrices. This choice of measurements can be interpreted as randomly sampling only a small subset of dug wells at each time step, instead of sampling the entire grid. Therefore, this framework offers groundwater surveyors a significant reduction in surveying effort without compromising the quality of the survey. © 2013 IEEE.
Hussain, Z.
Parallel Sparse Matrix - Vector Product
Alexandersen, Joe; Lazarov, Boyan Stefanov; Dammann, Bernd
This technical report contains a case study of a sparse matrix-vector product routine, implemented for parallel execution on a compute cluster with both pure MPI and hybrid MPI-OpenMP solutions. C++ classes for sparse data types were developed and the report shows how these class can be used...
Block matching sparsity regularization-based image reconstruction for incomplete projection data in computed tomography
Cai, Ailong; Li, Lei; Zheng, Zhizhong; Zhang, Hanming; Wang, Linyuan; Hu, Guoen; Yan, Bin
In medical imaging many conventional regularization methods, such as total variation or total generalized variation, impose strong prior assumptions which can only account for very limited classes of images. A more reasonable sparse representation frame for images is still badly needed. Visually understandable images contain meaningful patterns, and combinations or collections of these patterns can be utilized to form some sparse and redundant representations which promise to facilitate image reconstructions. In this work, we propose and study block matching sparsity regularization (BMSR) and devise an optimization program using BMSR for computed tomography (CT) image reconstruction for an incomplete projection set. The program is built as a constrained optimization, minimizing the L1-norm of the coefficients of the image in the transformed domain subject to data observation and positivity of the image itself. To solve the program efficiently, a practical method based on the proximal point algorithm is developed and analyzed. In order to accelerate the convergence rate, a practical strategy for tuning the BMSR parameter is proposed and applied. The experimental results for various settings, including real CT scanning, have verified the proposed reconstruction method showing promising capabilities over conventional regularization.
Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.
Deveci, Mehmet [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Trott, Christian Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.
Adaptive structured dictionary learning for image fusion based on group-sparse-representation
Yang, Jiajie; Sun, Bin; Luo, Chengwei; Wu, Yuzhong; Xu, Limei
Dictionary learning is the key process of sparse representation which is one of the most widely used image representation theories in image fusion. The existing dictionary learning method does not use the group structure information and the sparse coefficients well. In this paper, we propose a new adaptive structured dictionary learning algorithm and a l1-norm maximum fusion rule that innovatively utilizes grouped sparse coefficients to merge the images. In the dictionary learning algorithm, we do not need prior knowledge about any group structure of the dictionary. By using the characteristics of the dictionary in expressing the signal, our algorithm can automatically find the desired potential structure information that hidden in the dictionary. The fusion rule takes the physical meaning of the group structure dictionary, and makes activity-level judgement on the structure information when the images are being merged. Therefore, the fused image can retain more significant information. Comparisons have been made with several state-of-the-art dictionary learning methods and fusion rules. The experimental results demonstrate that, the dictionary learning algorithm and the fusion rule both outperform others in terms of several objective evaluation metrics.
Blind Signal Classification via Spare Coding
Blind Signal Classification via Sparse Coding Youngjune Gwon MIT Lincoln Laboratory gyj@ll.mit.edu Siamak Dastangoo MIT Lincoln Laboratory sia...achieve blind signal classification with no prior knowledge about signals (e.g., MCS, pulse shaping) in an arbitrary RF channel. Since modulated RF...classification method. Our results indicate that we can separate different classes of digitally modulated signals from blind sampling with 70.3% recall and 24.6
Financial signal processing and machine learning
Kulkarni,Sanjeev R; Dmitry M. Malioutov
The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analy...
Sparse approximation with bases
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Efficient convolutional sparse coding
Wohlberg, Brendt
Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.
Hyperspectral Unmixing with Robust Collaborative Sparse Regression
Chang Li
Full Text Available Recently, sparse unmixing (SU of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM, which ignores the possible nonlinear effects (i.e., nonlinearity. In this paper, we propose a new method named robust collaborative sparse regression (RCSR based on the robust LMM (rLMM for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.
Analysis of Block OMP using Block RIP
Wang, Jun; Li, Gang; Zhang, Hao; Wang, Xiqin
Orthogonal matching pursuit (OMP) is a canonical greedy algorithm for sparse signal reconstruction. When the signal of interest is block sparse, i.e., it has nonzero coefficients occurring in clusters, the block version of OMP algorithm (i.e., Block OMP) outperforms the conventional OMP. In this paper, we demonstrate that a new notion of block restricted isometry property (Block RIP), which is less stringent than standard restricted isometry property (RIP), can be used for a very straightforw...
An equilibrium-point model of electromyographic patterns during single-joint movements based on experimentally reconstructed control signals.
Latash, M L; Goodman, S R
The purpose of this work has been to develop a model of electromyographic (EMG) patterns during single-joint movements based on a version of the equilibrium-point hypothesis, a method for experimental reconstruction of the joint compliant characteristics, the dual-strategy hypothesis, and a kinematic model of movement trajectory. EMG patterns are considered emergent properties of hypothetical control patterns that are equally affected by the control signals and peripheral feedback reflecting actual movement trajectory. A computer model generated the EMG patterns based on simulated movement kinematics and hypothetical control signals derived from the reconstructed joint compliant characteristics. The model predictions have been compared to published recordings of movement kinematics and EMG patterns in a variety of movement conditions, including movements over different distances, at different speeds, against different-known inertial loads, and in conditions of possible unexpected decrease in the inertial load. Changes in task parameters within the model led to simulated EMG patterns qualitatively similar to the experimentally recorded EMG patterns. The model's predictive power compares it favourably to the existing models of the EMG patterns. Copyright © 1994. Published by Elsevier Ltd.
Image fusion using sparse overcomplete feature dictionaries
Brumby, Steven P.; Bettencourt, Luis; Kenyon, Garrett T.; Chartrand, Rick; Wohlberg, Brendt
Approaches for deciding what individuals in a population of visual system "neurons" are looking for using sparse overcomplete feature dictionaries are provided. A sparse overcomplete feature dictionary may be learned for an image dataset and a local sparse representation of the image dataset may be built using the learned feature dictionary. A local maximum pooling operation may be applied on the local sparse representation to produce a translation-tolerant representation of the image dataset. An object may then be classified and/or clustered within the translation-tolerant representation of the image dataset using a supervised classification algorithm and/or an unsupervised clustering algorithm.
A Two-Stage Framework for 3D Face Reconstruction from RGBD Images.
Wang, Kangkan; Wang, Xianwang; Pan, Zhigeng; Liu, Kai
This paper proposes a new approach for 3D face reconstruction with RGBD images from an inexpensive commodity sensor. The challenges we face are: 1) substantial random noise and corruption are present in low-resolution depth maps; and 2) there is high degree of variability in pose and face expression. We develop a novel two-stage algorithm that effectively maps low-quality depth maps to realistic face models. Each stage is targeted toward a certain type of noise. The first stage extracts sparse errors from depth patches through the data-driven local sparse coding, while the second stage smooths noise on the boundaries between patches and reconstructs the global shape by combining local shapes using our template-based surface refinement. Our approach does not require any markers or user interaction. We perform quantitative and qualitative evaluations on both synthetic and real test sets. Experimental results show that the proposed approach is able to produce high-resolution 3D face models with high accuracy, even if inputs are of low quality, and have large variations in viewpoint and face expression.
Manifold regularization for sparse unmixing of hyperspectral images.
Liu, Junmin; Zhang, Chunxia; Zhang, Jiangshe; Li, Huirong; Gao, Yuelin
Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression , ignore the intrinsic geometric structure in the hyperspectral data. In this paper, we propose a novel model, called manifold regularized collaborative sparse regression , by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.
Image quality in thoracic 4D cone-beam CT: A sensitivity analysis of respiratory signal, binning method, reconstruction algorithm, and projection angular spacing
Shieh, Chun-Chien; Kipritidis, John; O'Brien, Ricky T.; Keall, Paul J.; Kuncic, Zdenka
Purpose: Respiratory signal, binning method, and reconstruction algorithm are three major controllable factors affecting image quality in thoracic 4D cone-beam CT (4D-CBCT), which is widely used in image guided radiotherapy (IGRT). Previous studies have investigated each of these factors individually, but no integrated sensitivity analysis has been performed. In addition, projection angular spacing is also a key factor in reconstruction, but how it affects image quality is not obvious. An investigation of the impacts of these four factors on image quality can help determine the most effective strategy in improving 4D-CBCT for IGRT. Methods: Fourteen 4D-CBCT patient projection datasets with various respiratory motion features were reconstructed with the following controllable factors: (i) respiratory signal (real-time position management, projection image intensity analysis, or fiducial marker tracking), (ii) binning method (phase, displacement, or equal-projection-density displacement binning), and (iii) reconstruction algorithm [Feldkamp–Davis–Kress (FDK), McKinnon–Bates (MKB), or adaptive-steepest-descent projection-onto-convex-sets (ASD-POCS)]. The image quality was quantified using signal-to-noise ratio (SNR), contrast-to-noise ratio, and edge-response width in order to assess noise/streaking and blur. The SNR values were also analyzed with respect to the maximum, mean, and root-mean-squared-error (RMSE) projection angular spacing to investigate how projection angular spacing affects image quality. Results: The choice of respiratory signals was found to have no significant impact on image quality. Displacement-based binning was found to be less prone to motion artifacts compared to phase binning in more than half of the cases, but was shown to suffer from large interbin image quality variation and large projection angular gaps. Both MKB and ASD-POCS resulted in noticeably improved image quality almost 100% of the time relative to FDK. In addition, SNR
Shieh, Chun-Chien [Radiation Physics Laboratory, Sydney Medical School, University of Sydney, NSW 2006, Australia and Institute of Medical Physics, School of Physics, University of Sydney, NSW 2006 (Australia); Kipritidis, John; O'Brien, Ricky T.; Keall, Paul J., E-mail: paul.keall@sydney.edu.au [Radiation Physics Laboratory, Sydney Medical School, University of Sydney, NSW 2006 (Australia); Kuncic, Zdenka [Institute of Medical Physics, School of Physics, University of Sydney, NSW 2006 (Australia)
Enhancing Scalability of Sparse Direct Methods
Li, Xiaoye S.; Demmel, James; Grigori, Laura; Gu, Ming; Xia, Jianlin; Jardin, Steve; Sovinec, Carl; Lee, Lie-Quan
TOPS is providing high-performance, scalable sparse direct solvers, which have had significant impacts on the SciDAC applications, including fusion simulation (CEMM), accelerator modeling (COMPASS), as well as many other mission-critical applications in DOE and elsewhere. Our recent developments have been focusing on new techniques to overcome scalability bottleneck of direct methods, in both time and memory. These include parallelizing symbolic analysis phase and developing linear-complexity sparse factorization methods. The new techniques will make sparse direct methods more widely usable in large 3D simulations on highly-parallel petascale computers
Regression with Sparse Approximations of Data
Noorzad, Pardis; Sturm, Bob L.
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
Sparse adaptive filters for echo cancellation
Paleologu, Constantin
Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellati
First Gridded Spatial Field Reconstructions of Snow from Tree Rings
Coulthard, B. L.; Anchukaitis, K. J.; Pederson, G. T.; Alder, J. R.; Hostetler, S. W.; Gray, S. T.
Western North America's mountain snowpacks provide critical water resources for human populations and ecosystems. Warmer temperatures and changing precipitation patterns will increasingly alter the quantity, extent, and persistence of snow in coming decades. A comprehensive understanding of the causes and range of long-term variability in this system is required for forecasting future anomalies, but snowpack observations are limited and sparse. While individual tree ring-based annual snowpack reconstructions have been developed for specific regions and mountain ranges, we present here the first collection of spatially-explicit gridded field reconstructions of seasonal snowpack within the American Rocky Mountains. Capitalizing on a new western North American snow-sensitive network of over 700 tree-ring chronologies, as well as recent advances in PRISM-based snow modeling, our gridded reconstructions offer a full space-time characterization of snow and associated water resource fluctuations over several centuries. The quality of reconstructions is evaluated against existing observations, proxy-records, and an independently-developed first-order monthly snow model.
Direction-of-Arrival Estimation for Coherent Sources via Sparse Bayesian Learning
Zhang-Meng Liu
Full Text Available A spatial filtering-based relevance vector machine (RVM is proposed in this paper to separate coherent sources and estimate their directions-of-arrival (DOA, with the filter parameters and DOA estimates initialized and refined via sparse Bayesian learning. The RVM is used to exploit the spatial sparsity of the incident signals and gain improved adaptability to much demanding scenarios, such as low signal-to-noise ratio (SNR, limited snapshots, and spatially adjacent sources, and the spatial filters are introduced to enhance global convergence of the original RVM in the case of coherent sources. The proposed method adapts to arbitrary array geometry, and simulation results show that it surpasses the existing methods in DOA estimation performance.
Characterizing spatiotemporal information loss in sparse-sampling-based dynamic MRI for monitoring respiration-induced tumor motion in radiotherapy
Arai, Tatsuya J. [Department of Radiation Oncology, UT Southwestern Medical Center, Dallas, Texas 75390 (United States); Nofiele, Joris; Yuan, Qing [Department of Radiology, UT Southwestern Medical Center, Dallas, Texas 75390 (United States); Madhuranthakam, Ananth J.; Pedrosa, Ivan; Chopra, Rajiv [Department of Radiology, UT Southwestern Medical Center, Dallas, Texas 75390 (United States); Advanced Imaging Research Center, UT Southwestern Medical Center, Dallas, Texas 75390 (United States); Sawant, Amit, E-mail: amit.sawant@utsouthwestern.edu [Department of Radiation Oncology, UT Southwestern Medical Center, Dallas, Texas 75390 (United States); Department of Radiology, UT Southwestern Medical Center, Dallas, Texas 75390 (United States); Department of Radiation Oncology, University of Maryland School of Medicine, Baltimore, Maryland, 21201 (United States)
Purpose: Sparse-sampling and reconstruction techniques represent an attractive strategy to achieve faster image acquisition speeds, while maintaining adequate spatial resolution and signal-to-noise ratio in rapid magnetic resonance imaging (MRI). The authors investigate the use of one such sequence, broad-use linear acquisition speed-up technique (k-t BLAST) in monitoring tumor motion for thoracic and abdominal radiotherapy and examine the potential trade-off between increased sparsification (to increase imaging speed) and the potential loss of "true� information due to greater reliance on a priori information. Methods: Lung tumor motion trajectories in the superior–inferior direction, previously recorded from ten lung cancer patients, were replayed using a motion phantom module driven by an MRI-compatible motion platform. Eppendorf test tubes filled with water which serve as fiducial markers were placed in the phantom. The modeled rigid and deformable motions were collected in a coronal image slice using balanced fast field echo in conjunction with k-t BLAST. Root mean square (RMS) error was used as a metric of spatial accuracy as measured trajectories were compared to input data. The loss of spatial information was characterized for progressively increasing acceleration factor from 1 to 16; the resultant sampling frequency was increased approximately from 2.5 to 19 Hz when the principal direction of the motion was set along frequency encoding direction. In addition to the phantom study, respiration-induced tumor motions were captured from two patients (kidney tumor and lung tumor) at 13 Hz over 49 s to demonstrate the impact of high speed motion monitoring over multiple breathing cycles. For each subject, the authors compared the tumor centroid trajectory as well as the deformable motion during free breathing. Results: In the rigid and deformable phantom studies, the RMS error of target tracking at the acquisition speed of 19 Hz was approximately 0.3–0
A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing
Zhu, Yansong; Jha, Abhinav K.; Dreyer, Jakob K.
Fluorescence molecular tomography (FMT) is a promising tool for real time in vivo quantification of neurotransmission (NT) as we pursue in our BRAIN initiative effort. However, the acquired image data are noisy and the reconstruction problem is ill-posed. Further, while spatial sparsity of the NT...... matrix coherence. The resultant image data are input to a homotopy-based reconstruction strategy that exploits sparsity via â""1 regularization. The reconstructed image is then input to a maximum-likelihood expectation maximization (MLEM) algorithm that retains the sparseness of the input estimate...... and improves upon the quantitation by accurate Poisson noise modeling. The proposed reconstruction method was evaluated in a three-dimensional simulated setup with fluorescent sources in a cuboidal scattering medium with optical properties simulating human brain cortex (reduced scattering coefficient: 9.2 cm-1...
Automatic Texture Optimization for 3D Urban Reconstruction
LI Ming
Full Text Available In order to solve the problem of texture optimization in 3D city reconstruction by using multi-lens oblique images, the paper presents a method of seamless texture model reconstruction. At first, it corrects the radiation information of images by camera response functions and image dark channel. Then, according to the corresponding relevance between terrain triangular mesh surface model to image, implements occlusion detection by sparse triangulation method, and establishes the triangles' texture list of visible. Finally, combines with triangles' topology relationship in 3D triangular mesh surface model and means and variances of image, constructs a graph-cuts-based texture optimization algorithm under the framework of MRF(Markov random filed, to solve the discrete label problem of texture optimization selection and clustering, ensures the consistency of the adjacent triangles in texture mapping, achieves the seamless texture reconstruction of city. The experimental results verify the validity and superiority of our proposed method.
Parallel sparse direct solver for integrated circuit simulation
Chen, Xiaoming; Yang, Huazhong
This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...
Analysis of impulse signals with Hylaty ELF station
Kulak, A.; Mlynarczyk, J.; Ostrowski, M.; Kubisz, J.; Michalec, A.
Lighting discharges generate electromagnetic field pulses that propagate in the Earth-ionosphere waveguide. The attenuation in the ELF range is so small that the pulses originating from strong atmospheric discharges can be observed even several thousand kilometers away from the individual discharge. The recorded waveform depends on the discharge process, the Earth-ionosphere waveguide properties on the source-receiver path, and the transfer function of the receiver. If the distance from the source is known, an inverse method can be used for reconstructing the current moment waveform and the charge moment of the discharge. In order to reconstruct the source parameters from the recorded signal a reliable model of the radio wave propagation in the Earth-ionosphere waveguide as well as practical signal processing techniques are necessary. We present two methods, both based on analytical formulas. The first method allows for fast calculation of the charge moment of relatively short atmospheric discharges. It is based on peak amplitude measurement of the recorded magnetic component of the ELF EM field and it takes into account the receiver characteristics. The second method, called "inverse channel method" allows reconstructing the complete current moment waveform of strong atmospheric discharges that exhibit the continuing current phase, such as Gigantic Jets and Sprites. The method makes it possible to fully remove from the observed waveform the distortions related to the receiver's impulse response as well as the influence of the Earth-ionosphere propagation channel. Our ELF station is equipped with two magnetic antennas for Bx and By components measurement in the 0.03 to 55 Hz frequency range. ELF Data recording is carried out since 1993, with continuous data acquisition since 2005. The station features low noise level and precise timing. It is battery powered and located in the sparsely populated area, far from major electric power lines, which results in high
Biclustering via Sparse Singular Value Decomposition
Lee, Mihee
Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.
SVM-Based Spectral Analysis for Heart Rate from Multi-Channel WPPG Sensor Signals
Jiping Xiong
Full Text Available Although wrist-type photoplethysmographic (hereafter referred to as WPPG sensor signals can measure heart rate quite conveniently, the subjects' hand movements can cause strong motion artifacts, and then the motion artifacts will heavily contaminate WPPG signals. Hence, it is challenging for us to accurately estimate heart rate from WPPG signals during intense physical activities. The WWPG method has attracted more attention thanks to the popularity of wrist-worn wearable devices. In this paper, a mixed approach called Mix-SVM is proposed, it can use multi-channel WPPG sensor signals and simultaneous acceleration signals to measurement heart rate. Firstly, we combine the principle component analysis and adaptive filter to remove a part of the motion artifacts. Due to the strong relativity between motion artifacts and acceleration signals, the further denoising problem is regarded as a sparse signals reconstruction problem. Then, we use a spectrum subtraction method to eliminate motion artifacts effectively. Finally, the spectral peak corresponding to heart rate is sought by an SVM-based spectral analysis method. Through the public PPG database in the 2015 IEEE Signal Processing Cup, we acquire the experimental results, i.e., the average absolute error was 1.01 beat per minute, and the Pearson correlation was 0.9972. These results also confirm that the proposed Mix-SVM approach has potential for multi-channel WPPG-based heart rate estimation in the presence of intense physical exercise.
Sparse sampling and reconstruction for electron and scanning probe microscope imaging
Anderson, Hyrum; Helms, Jovana; Wheeler, Jason W.; Larson, Kurt W.; Rohrer, Brandon R.
Systems and methods for conducting electron or scanning probe microscopy are provided herein. In a general embodiment, the systems and methods for conducting electron or scanning probe microscopy with an undersampled data set include: driving an electron beam or probe to scan across a sample and visit a subset of pixel locations of the sample that are randomly or pseudo-randomly designated; determining actual pixel locations on the sample that are visited by the electron beam or probe; and processing data collected by detectors from the visits of the electron beam or probe at the actual pixel locations and recovering a reconstructed image of the sample.
Robust Face Recognition Via Gabor Feature and Sparse Representation
Hao Yu-Juan
Full Text Available Sparse representation based on compressed sensing theory has been widely used in the field of face recognition, and has achieved good recognition results. but the face feature extraction based on sparse representation is too simple, and the sparse coefficient is not sparse. In this paper, we improve the classification algorithm based on the fusion of sparse representation and Gabor feature, and then improved algorithm for Gabor feature which overcomes the problem of large dimension of the vector dimension, reduces the computation and storage cost, and enhances the robustness of the algorithm to the changes of the environment.The classification efficiency of sparse representation is determined by the collaborative representation,we simplify the sparse constraint based on L1 norm to the least square constraint, which makes the sparse coefficients both positive and reduce the complexity of the algorithm. Experimental results show that the proposed method is robust to illumination, facial expression and pose variations of face recognition, and the recognition rate of the algorithm is improved.
Sparse Learning with Stochastic Composite Optimization.
Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei
In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).
Shearlets and Optimally Sparse Approximations
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....
A sparse version of IGA solvers
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
Simulation and experimental studies of three-dimensional (3D) image reconstruction from insufficient sampling data based on compressed-sensing theory for potential applications to dental cone-beam CT
Je, U.K.; Lee, M.S.; Cho, H.S.; Hong, D.K.; Park, Y.O.; Park, C.K.; Cho, H.M.; Choi, S.I.; Woo, T.H.
In practical applications of three-dimensional (3D) tomographic imaging, there are often challenges for image reconstruction from insufficient sampling data. In computed tomography (CT), for example, image reconstruction from sparse views and/or limited-angle (<360°) views would enable fast scanning with reduced imaging doses to the patient. In this study, we investigated and implemented a reconstruction algorithm based on the compressed-sensing (CS) theory, which exploits the sparseness of the gradient image with substantially high accuracy, for potential applications to low-dose, high-accurate dental cone-beam CT (CBCT). We performed systematic simulation works to investigate the image characteristics and also performed experimental works by applying the algorithm to a commercially-available dental CBCT system to demonstrate its effectiveness for image reconstruction in insufficient sampling problems. We successfully reconstructed CBCT images of superior accuracy from insufficient sampling data and evaluated the reconstruction quality quantitatively. Both simulation and experimental demonstrations of the CS-based reconstruction from insufficient data indicate that the CS-based algorithm can be applied directly to current dental CBCT systems for reducing the imaging doses and further improving the image quality
Shieh, Chun-Chien; Kipritidis, John; O'Brien, Ricky T.; Kuncic, Zdenka; Keall, Paul J.
Purpose: Respiratory signal, binning method, and reconstruction algorithm are three major controllable factors affecting image quality in thoracic 4D cone-beam CT (4D-CBCT), which is widely used in image guided radiotherapy (IGRT). Previous studies have investigated each of these factors individually, but no integrated sensitivity analysis has been performed. In addition, projection angular spacing is also a key factor in reconstruction, but how it affects image quality is not obvious. An inv...
Population coding in sparsely connected networks of noisy neurons.
Tripp, Bryan P; Orchard, Jeff
This study examines the relationship between population coding and spatial connection statistics in networks of noisy neurons. Encoding of sensory information in the neocortex is thought to require coordinated neural populations, because individual cortical neurons respond to a wide range of stimuli, and exhibit highly variable spiking in response to repeated stimuli. Population coding is rooted in network structure, because cortical neurons receive information only from other neurons, and because the information they encode must be decoded by other neurons, if it is to affect behavior. However, population coding theory has often ignored network structure, or assumed discrete, fully connected populations (in contrast with the sparsely connected, continuous sheet of the cortex). In this study, we modeled a sheet of cortical neurons with sparse, primarily local connections, and found that a network with this structure could encode multiple internal state variables with high signal-to-noise ratio. However, we were unable to create high-fidelity networks by instantiating connections at random according to spatial connection probabilities. In our models, high-fidelity networks required additional structure, with higher cluster factors and correlations between the inputs to nearby neurons.
Population Coding in Sparsely Connected Networks of Noisy Neurons
Bryan Patrick Tripp
Full Text Available This study examines the relationship between population coding and spatial connection statistics in networks of noisy neurons. Encoding of sensory information in the neocortex is thought to require coordinated neural populations, because individual cortical neurons respond to a wide range of stimuli, and exhibit highly variable spiking in response to repeated stimuli. Population coding is rooted in network structure, because cortical neurons receive information only from other neurons, and because the information they encode must be decoded by other neurons, if it is to affect behaviour. However, population coding theory has often ignored network structure, or assumed discrete, fully-connected populations (in contrast with the sparsely connected, continuous sheet of the cortex. In this study, we model a sheet of cortical neurons with sparse, primarily local connections, and find that a network with this structure can encode multiple internal state variables with high signal-to-noise ratio. However, in our model, although connection probability varies with the distance between neurons, we find that the connections cannot be instantiated at random according to these probabilities, but must have additional structure if information is to be encoded with high fidelity.
Language Recognition via Sparse Coding
explanation is that sparse coding can achieve a near-optimal approximation of much complicated nonlinear relationship through local and piecewise linear...training examples, where x(i) ∈ RN is the ith example in the batch. Optionally, X can be normalized and whitened before sparse coding for better result...normalized input vectors are then ZCA- whitened [20]. Em- pirically, we choose ZCA- whitening over PCA- whitening , and there is no dimensionality reduction
Free-breathing Sparse Sampling Cine MR Imaging with Iterative Reconstruction for the Assessment of Left Ventricular Function and Mass at 3.0 T.
Sudarski, Sonja; Henzler, Thomas; Haubenreisser, Holger; Dösch, Christina; Zenge, Michael O; Schmidt, Michaela; Nadar, Mariappan S; Borggrefe, Martin; Schoenberg, Stefan O; Papavassiliu, Theano
Purpose To prospectively evaluate the accuracy of left ventricle (LV) analysis with a two-dimensional real-time cine true fast imaging with steady-state precession (trueFISP) magnetic resonance (MR) imaging sequence featuring sparse data sampling with iterative reconstruction (SSIR) performed with and without breath-hold (BH) commands at 3.0 T. Materials and Methods Ten control subjects (mean age, 35 years; range, 25-56 years) and 60 patients scheduled to undergo a routine cardiac examination that included LV analysis (mean age, 58 years; range, 20-86 years) underwent a fully sampled segmented multiple BH cine sequence (standard of reference) and a prototype undersampled SSIR sequence performed during a single BH and during free breathing (non-BH imaging). Quantitative analysis of LV function and mass was performed. Linear regression, Bland-Altman analysis, and paired t testing were performed. Results Similar to the results in control subjects, analysis of the 60 patients showed excellent correlation with the standard of reference for single-BH SSIR (r = 0.93-0.99) and non-BH SSIR (r = 0.92-0.98) for LV ejection fraction (EF), volume, and mass (P 3.0 T is noninferior to the standard of reference irrespective of BH commands. LV mass, however, is overestimated with SSIR. © RSNA, 2016 Online supplemental material is available for this article.
Simultaneous Channel and Feature Selection of Fused EEG Features Based on Sparse Group Lasso
Jin-Jia Wang
Full Text Available Feature extraction and classification of EEG signals are core parts of brain computer interfaces (BCIs. Due to the high dimension of the EEG feature vector, an effective feature selection algorithm has become an integral part of research studies. In this paper, we present a new method based on a wrapped Sparse Group Lasso for channel and feature selection of fused EEG signals. The high-dimensional fused features are firstly obtained, which include the power spectrum, time-domain statistics, AR model, and the wavelet coefficient features extracted from the preprocessed EEG signals. The wrapped channel and feature selection method is then applied, which uses the logistical regression model with Sparse Group Lasso penalized function. The model is fitted on the training data, and parameter estimation is obtained by modified blockwise coordinate descent and coordinate gradient descent method. The best parameters and feature subset are selected by using a 10-fold cross-validation. Finally, the test data is classified using the trained model. Compared with existing channel and feature selection methods, results show that the proposed method is more suitable, more stable, and faster for high-dimensional feature fusion. It can simultaneously achieve channel and feature selection with a lower error rate. The test accuracy on the data used from international BCI Competition IV reached 84.72%.
Tunable Sparse Network Coding for Multicast Networks
Feizi, Soheil; Roetter, Daniel Enrique Lucani; Sørensen, Chres Wiant
This paper shows the potential and key enabling mechanisms for tunable sparse network coding, a scheme in which the density of network coded packets varies during a transmission session. At the beginning of a transmission session, sparsely coded packets are transmitted, which benefits decoding...... complexity. At the end of a transmission, when receivers have accumulated degrees of freedom, coding density is increased. We propose a family of tunable sparse network codes (TSNCs) for multicast erasure networks with a controllable trade-off between completion time performance to decoding complexity...... a mechanism to perform efficient Gaussian elimination over sparse matrices going beyond belief propagation but maintaining low decoding complexity. Supporting simulation results are provided showing the trade-off between decoding complexity and completion time....
Sparse PCA with Oracle Property.
Gu, Quanquan; Wang, Zhaoran; Liu, Han
In this paper, we study the estimation of the k -dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank- k , and attains a [Formula: see text] statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.
Zhang, Tianzhu; Yang, Ming-Hsuan; Ahuja, Narendra; Ghanem, Bernard; Yan, Shuicheng; Xu, Changsheng; Liu, Si
candidate. We show that our SST algorithm accommodates most existing sparse trackers with the respective merits. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed SST algorithm performs
Technique detection software for Sparse Matrices
KHAN Muhammad Taimoor
Full Text Available Sparse storage formats are techniques for storing and processing the sparse matrix data efficiently. The performance of these storage formats depend upon the distribution of non-zeros, within the matrix in different dimensions. In order to have better results we need a technique that suits best the organization of data in a particular matrix. So the decision of selecting a better technique is the main step towards improving the system's results otherwise the efficiency can be decreased. The purpose of this research is to help identify the best storage format in case of reduced storage size and high processing efficiency for a sparse matrix.
Structure-aware Local Sparse Coding for Visual Tracking
Qi, Yuankai
Sparse coding has been applied to visual tracking and related vision problems with demonstrated success in recent years. Existing tracking methods based on local sparse coding sample patches from a target candidate and sparsely encode these using a dictionary consisting of patches sampled from target template images. The discriminative strength of existing methods based on local sparse coding is limited as spatial structure constraints among the template patches are not exploited. To address this problem, we propose a structure-aware local sparse coding algorithm which encodes a target candidate using templates with both global and local sparsity constraints. For robust tracking, we show local regions of a candidate region should be encoded only with the corresponding local regions of the target templates that are the most similar from the global view. Thus, a more precise and discriminative sparse representation is obtained to account for appearance changes. To alleviate the issues with tracking drifts, we design an effective template update scheme. Extensive experiments on challenging image sequences demonstrate the effectiveness of the proposed algorithm against numerous stateof- the-art methods.
Low dose CT reconstruction via L1 norm dictionary learning using alternating minimization algorithm and balancing principle.
Wu, Junfeng; Dai, Fang; Hu, Gang; Mou, Xuanqin
Excessive radiation exposure in computed tomography (CT) scans increases the chance of developing cancer and has become a major clinical concern. Recently, statistical iterative reconstruction (SIR) with l0-norm dictionary learning regularization has been developed to reconstruct CT images from the low dose and few-view dataset in order to reduce radiation dose. Nonetheless, the sparse regularization term adopted in this approach is l0-norm, which cannot guarantee the global convergence of the proposed algorithm. To address this problem, in this study we introduced the l1-norm dictionary learning penalty into SIR framework for low dose CT image reconstruction, and developed an alternating minimization algorithm to minimize the associated objective function, which transforms CT image reconstruction problem into a sparse coding subproblem and an image updating subproblem. During the image updating process, an efficient model function approach based on balancing principle is applied to choose the regularization parameters. The proposed alternating minimization algorithm was evaluated first using real projection data of a sheep lung CT perfusion and then using numerical simulation based on sheep lung CT image and chest image. Both visual assessment and quantitative comparison using terms of root mean square error (RMSE) and structural similarity (SSIM) index demonstrated that the new image reconstruction algorithm yielded similar performance with l0-norm dictionary learning penalty and outperformed the conventional filtered backprojection (FBP) and total variation (TV) minimization algorithms.
Integration of sparse multi-modality representation and geometrical constraint for isointense infant brain segmentation.
Wang, Li; Shi, Feng; Li, Gang; Lin, Weili; Gilmore, John H; Shen, Dinggang
Segmentation of infant brain MR images is challenging due to insufficient image quality, severe partial volume effect, and ongoing maturation and myelination process. During the first year of life, the signal contrast between white matter (WM) and gray matter (GM) in MR images undergoes inverse changes. In particular, the inversion of WM/GM signal contrast appears around 6-8 months of age, where brain tissues appear isointense and hence exhibit extremely low tissue contrast, posing significant challenges for automated segmentation. In this paper, we propose a novel segmentation method to address the above-mentioned challenge based on the sparse representation of the complementary tissue distribution information from T1, T2 and diffusion-weighted images. Specifically, we first derive an initial segmentation from a library of aligned multi-modality images with ground-truth segmentations by using sparse representation in a patch-based fashion. The segmentation is further refined by the integration of the geometrical constraint information. The proposed method was evaluated on 22 6-month-old training subjects using leave-one-out cross-validation, as well as 10 additional infant testing subjects, showing superior results in comparison to other state-of-the-art methods.
Aggregate Measures of Watershed Health from Reconstructed ...
Risk-based indices such as reliability, resilience, and vulnerability (R-R-V), have the potential to serve as watershed health assessment tools. Recent research has demonstrated the applicability of such indices for water quality (WQ) constituents such as total suspended solids and nutrients on an individual basis. However, the calculations can become tedious when time-series data for several WQ constituents have to be evaluated individually. Also, comparisons between locations with different sets of constituent data can prove difficult. In this study, data reconstruction using relevance vector machine algorithm was combined with dimensionality reduction via variational Bayesian noisy principal component analysis to reconstruct and condense sparse multidimensional WQ data sets into a single time series. The methodology allows incorporation of uncertainty in both the reconstruction and dimensionality-reduction steps. The R-R-V values were calculated using the aggregate time series at multiple locations within two Indiana watersheds. Results showed that uncertainty present in the reconstructed WQ data set propagates to the aggregate time series and subsequently to the aggregate R-R-V values as well. serving as motivating examples. Locations with different WQ constituents and different standards for impairment were successfully combined to provide aggregate measures of R-R-V values. Comparisons with individual constituent R-R-V values showed that v
Paleoclimate Signals and Temperature Reconstructions for the Northeastern United States using Atlantic White Cedar Tree-Rings
Pearl, J. K.; Anchukaitis, K. J.; Pederson, N.; Donnelly, J. P.
High-resolution paleoclimate records of the Common Era are essential for improving detection and attribution of internal and forced climate system responses. The densely populated northeastern United States is at risk from impending climate shifts as well as sea level rise. Here we present a new network of annually resolved proxy data from Atlantic white cedar trees throughout the northeastern United States. Ring width variability reflects winter through summer temperatures at inland sites north of New Jersey. Climate signals embedded in the full network are evaluated for their potential to provide reconstructions of both temperature and drought variability. We demonstrate skillful climate reconstructions for the last several centuries and the potential to use subfossil samples to extend these records over the Common Era. Our tree-ring network provides the long-term context at multidecadal and centennial time scales for the large-scale ocean-atmospheric processes that influence the climate of the region.
Massive Asynchronous Parallelization of Sparse Matrix Factorizations
Chow, Edmond [Georgia Inst. of Technology, Atlanta, GA (United States)
Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.
Charge reconstruction in large-area photomultipliers
Grassi, M.; Montuschi, M.; Baldoncini, M.; Mantovani, F.; Ricci, B.; Andronico, G.; Antonelli, V.; Bellato, M.; Bernieri, E.; Brigatti, A.; Brugnera, R.; Budano, A.; Buscemi, M.; Bussino, S.; Caruso, R.; Chiesa, D.; Corti, D.; Dal Corso, F.; Ding, X. F.; Dusini, S.; Fabbri, A.; Fiorentini, G.; Ford, R.; Formozov, A.; Galet, G.; Garfagnini, A.; Giammarchi, M.; Giaz, A.; Insolia, A.; Isocrate, R.; Lippi, I.; Longhitano, F.; Lo Presti, D.; Lombardi, P.; Marini, F.; Mari, S. M.; Martellini, C.; Meroni, E.; Mezzetto, M.; Miramonti, L.; Monforte, S.; Nastasi, M.; Ortica, F.; Paoloni, A.; Parmeggiano, S.; Pedretti, D.; Pelliccia, N.; Pompilio, R.; Previtali, E.; Ranucci, G.; Re, A. C.; Romani, A.; Saggese, P.; Salamanna, G.; Sawy, F. H.; Settanta, G.; Sisti, M.; Sirignano, C.; Spinetti, M.; Stanco, L.; Strati, V.; Verde, G.; Votano, L.
Large-area PhotoMultiplier Tubes (PMT) allow to efficiently instrument Liquid Scintillator (LS) neutrino detectors, where large target masses are pivotal to compensate for neutrinos' extremely elusive nature. Depending on the detector light yield, several scintillation photons stemming from the same neutrino interaction are likely to hit a single PMT in a few tens/hundreds of nanoseconds, resulting in several photoelectrons (PEs) to pile-up at the PMT anode. In such scenario, the signal generated by each PE is entangled to the others, and an accurate PMT charge reconstruction becomes challenging. This manuscript describes an experimental method able to address the PMT charge reconstruction in the case of large PE pile-up, providing an unbiased charge estimator at the permille level up to 15 detected PEs. The method is based on a signal filtering technique (Wiener filter) which suppresses the noise due to both PMT and readout electronics, and on a Fourier-based deconvolution able to minimize the influence of signal distortions—such as an overshoot. The analysis of simulated PMT waveforms shows that the slope of a linear regression modeling the relation between reconstructed and true charge values improves from 0.769 ± 0.001 (without deconvolution) to 0.989 ± 0.001 (with deconvolution), where unitary slope implies perfect reconstruction. A C++ implementation of the charge reconstruction algorithm is available online at [1].
Sparse Representation Based Range-Doppler Processing for Integrated OFDM Radar-Communication Networks
Bo Kong
Full Text Available In an integrated radar-communication network, multiuser access techniques with minimal performance degradation and without range-Doppler ambiguities are required, especially in a dense user environment. In this paper, a multiuser access scheme with random subcarrier allocation mechanism is proposed for orthogonal frequency division multiplexing (OFDM based integrated radar-communication networks. The expression of modulation Symbol-Domain method combined with sparse representation (SR for range-Doppler estimation is introduced and a parallel reconstruction algorithm is employed. The radar target detection performance is improved with less spectrum occupation. Additionally, a Doppler frequency detector is exploited to decrease the computational complexity. Numerical simulations show that the proposed method outperforms the traditional modulation Symbol-Domain method under ideal and realistic nonideal scenarios.
Integration of sparse electrophysiological measurements with preoperative MRI using 3D surface estimation in deep brain stimulation surgery
Husch, Andreas; Gemmar, Peter; Thunberg, Johan; Hertel, Frank
Intraoperative microelectrode recordings (MER) have been used for several decades to guide neurosurgeons during the implantation of Deep Brain Stimulation (DBS) electrodes, especially when targeting the subthalamic nucleus (STN) to suppress the symptoms of Parkinson's Disease. The standard approach is to use an array of up to five MER electrodes in a fixed configuration. Interpretation of the recorded signals yields a spatially very sparse set of information about the morphology of the respective brain structures in the targeted area. However, no aid is currently available for surgeons to intraoperatively integrate this information with other data available on the patient's individual morphology (e.g. MR imaging data used for surgical planning). This integration might allow surgeons to better determine the most probable position of the electrodes within the target structure during surgery. This paper suggests a method for reconstructing a surface patch from the sparse MER dataset utilizing additional a priori knowledge about the geometrical configuration of the measurement electrodes. The conventional representation of MER measurements as intervals of target region/non-target region is therefore transformed into an equivalent boundary set representation, allowing ecient point-based calculations. Subsequently, the problem is to integrate the resulting patch with a preoperative model of the target structure, which can be formulated as registration problem minimizing a distance measure between the two surfaces. When restricting this registration procedure to translations, which is reasonable given certain geometric considerations, the problem can be solved globally by employing an exhaustive search with arbitrary precision in polynomial time. The proposed method is demonstrated using bilateral STN/Substantia Nigra segmentation data from preoperative MRIs of 17 Patients with simulated MER electrode placement. When using simulated data of heavily perturbed electrodes
A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction.
Lu, Hongyang; Wei, Jingbo; Liu, Qiegen; Wang, Yuhao; Deng, Xiaohua
Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.
Validation of a raw data-based synchronization signal (kymogram) for phase-correlated cardiac image reconstruction
Ertel, Dirk; Kachelriess, Marc; Kalender, Willi A.; Pflederer, Tobias; Achenbach, Stephan; Steffen, Peter
Phase-correlated reconstruction is commonly used in computed tomography (CT)-based cardiac imaging. Alternatively to the commonly used ECG, the raw data-based kymogram function can be used as a synchronization signal. We used raw data of 100 consecutive patient exams to compare the performance of kymogram function to the ECG signal. For objective validation the correlation of the ECG and the kymogram was assessed. Additionally, we performed a double-blinded comparison of ECG-based and kymogram-based phase-correlated images. The two synchronization signals showed good correlation indicated by a mean difference in the detected heart rate of negligible 0.2 bpm. The mean image quality score was 2.0 points for kymogram-correlated images and 2.3 points for ECG-correlated images, respectively (3: best; 0: worst). The kymogram and the ECG provided images adequate for diagnosis for 93 and 97 patients, respectively. For 50% of the datasets the kymogram provided an equivalent or even higher image quality compared with the ECG signal. We conclude that an acceptable image quality can be assured in most cases by the kymogram. Improvements of image quality by the kymogram function were observed in a noticeable number of cases. The kymogram can serve as a backup solution when an ECG is not available or lacking in quality. (orig.)