A Data-Driven and Distributed Approach to Sparse Signal Representation and Recovery
In this paper, we focus on two challenges which offset the promise of sparse signal representation, sensing, and recovery. First, real-world signals can seldom be described as perfectly sparse vectors in a known basis, and traditionally used random measurement schemes are seldom optimal for sensing them. Second, existing signal recovery algorithms are usually not fast enough to make them applicable to real-time problems. In this paper, we address these two challenges by presenting a novel framework based on deep learning. For the first challenge, we cast the problem of finding informative measurements by using a maximum likelihood (ML) formulation and show how we can build a data-driven dimensionality reduction protocol for sensing signals using convolutional architectures. For the second challenge, we discuss and analyze a novel parallelization scheme and show it significantly speeds-up the signal recovery process. We demonstrate the significant improvement our method obtains over competing methods through a series of experiments.
 Authors case the problem of finding informative measurements by using a maximum likelihood formulation and show how a data-driven dimensionality reduction protocol is built for sensing signals using convolutional architectures. A novel parallelization scheme is discussed and analyzed for speeding up the signal recovery process. Previous works have been proposed to jointly learn the signal sensing and reconstruction algorithm using convolutional networks. Authors do not consider them as the baseline methods due to the fact that the blocky reconstruction approach is unrealistic such as MRI. However, there is no empirical result to support his conclusion. In addition, the comparisons to these methods can further convince the readers about the advantage of the proposed method. It is not clear where the maximum deviation from isometry in Algorithm 1 is discussed since the MSE is used as a loss function. Authors provided theoretical insights for the proposed algorithm. It indicates that the lower-bound of the mutual information is maximized and minimizing the mean squared error is a special case, but it is unclear why this can provide theoretical guarantee for the proposed method. More details are good for the connections between the theory and the proposed algorithm. One of the contributions in this paper is the speed, so the results on the speed should be put in the main paper.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
A Data-Driven and Distributed Approach to Sparse Signal Representation and Recovery
In this paper, we focus on two challenges which offset the promise of sparse signal representation, sensing, and recovery. First, real-world signals can seldom be described as perfectly sparse vectors in a known basis, and traditionally used random measurement schemes are seldom optimal for sensing them. Second, existing signal recovery algorithms are usually not fast enough to make them applicable to real-time problems. In this paper, we address these two challenges by presenting a novel framework based on deep learning. For the first challenge, we cast the problem of finding informative measurements by using a maximum likelihood (ML) formulation and show how we can build a data-driven dimensionality reduction protocol for sensing signals using convolutional architectures. For the second challenge, we discuss and analyze a novel parallelization scheme and show it significantly speeds-up the signal recovery process. We demonstrate the significant improvement our method obtains over competing methods through a series of experiments.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 Authors case the problem of finding informative measurements by using a maximum likelihood formulation and show how a data-driven dimensionality reduction protocol is built for sensing signals using convolutional architectures. A novel parallelization scheme is discussed and analyzed for speeding up the signal recovery process. Previous works have been proposed to jointly learn the signal sensing and reconstruction algorithm using convolutional networks. Authors do not consider them as the baseline methods due to the fact that the blocky reconstruction approach is unrealistic such as MRI. However, there is no empirical result to support his conclusion. In addition, the comparisons to these methods can further convince the readers about the advantage of the proposed method. It is not clear where the maximum deviation from isometry in Algorithm 1 is discussed since the MSE is used as a loss function. Authors provided theoretical insights for the proposed algorithm. It indicates that the lower-bound of the mutual information is maximized and minimizing the mean squared error is a special case, but it is unclear why this can provide theoretical guarantee for the proposed method. More details are good for the connections between the theory and the proposed algorithm. One of the contributions in this paper is the speed, so the results on the speed should be put in the main paper.
assistant
 Authors case the problem of finding informative measurements by using a maximum likelihood formulation and show how a data-driven dimensionality reduction protocol is built for sensing signals using convolutional architectures. A novel parallelization scheme is discussed and analyzed for speeding up the signal recovery process. Previous works have been proposed to jointly learn the signal sensing and reconstruction algorithm using convolutional networks. Authors do not consider them as the baseline methods due to the fact that the blocky reconstruction approach is unrealistic such as MRI. However, there is no empirical result to support his conclusion. In addition, the comparisons to these methods can further convince the readers about the advantage of the proposed method. It is not clear where the maximum deviation from isometry in Algorithm 1 is discussed since the MSE is used as a loss function. Authors provided theoretical insights for the proposed algorithm. It indicates that the lower-bound of the mutual information is maximized and minimizing the mean squared error is a special case, but it is unclear why this can provide theoretical guarantee for the proposed method. More details are good for the connections between the theory and the proposed algorithm. One of the contributions in this paper is the speed, so the results on the speed should be put in the main paper.