Learning Parametric Sparse Models for Image Super-Resolution
Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR). Existing SR methods either learn the prior from the low/high-resolution patch pairs or estimate the prior models from the input low-resolution (LR) image. Specifically, high-frequency details are learned in the former methods. Though effective, they are heuristic and have limitations in dealing with blurred LR images; while the latter suffers from the limitations of frequency aliasing. In this paper, we propose to combine those two lines of ideas for image super-resolution. More specifically, the parametric sparse prior of the desirable high-resolution (HR) image patches are learned from both the input low-resolution (LR) image and a training image dataset. With the learned sparse priors, the sparse codes and thus the HR image patches can be accurately recovered by solving a sparse coding problem. Experimental results show that the proposed SR method outperforms existing state-of-the-art methods in terms of both subjective and objective image qualities.
The proposed solution to single image super-resolution starts from and is inspired by [14] and [4] to design a method which employs sparse priors learned from both training images and input LR image and learned mapping functions between LR patches and the sparse codes of the preferable HR patches.
The method is novel, the performance is impressive on 3 standard datasets, and the paper reads well.  My concerns are expressed below and hopefully will be considered for improving the paper.  1) The parameters need to be not evaluated or discussed; at least some of them should be discussed if not supported by experiments.  2) In Table 1, I think that the SCSR method is the one from [2] and not [3]. why not having the results for x2, x4?  3) In Table 1, the PSNR/SSIM values for A+[7] and BSD100 are computed after saving to JPEG compressed images, while for the other methods (SRCNN, KK, NCSR) before.  In the following papers (appeared first in 2015 on arXiv) are reported better numbers for A+: [Ref1] Timofte et al, Seven ways to improve example-based single image super resolution, CVPR 2016 [Ref2] Kim et al, Accurate image super-resolution using very deep convolutional networks, CVPR 2016  4) Combining internal and external information for superior restoration performance is not new; It was shown, among others, in [Ref1] for super-resolution, and by (Mosseri et al, ICCP 2013) for denoising.  5) The experiment from 5.2, Tab. 2, is questionable. For a fair comparison it is necessary to report also the results for the example-based methods [3,7,8,10] after retraining for the conditions from the test.   6) I find necessary a discussion and comparison in run-times and/or time complexity of the methods. How much slower is the proposed method when compared with NCSR, A+ or SRCNN?