Understanding Compressive Sensing and Sparse Representation-Based Super-Resolution

Abstract

Recently, compressive sensing (CS) has emerged as a powerful tool for solving a class of inverse/underdetermined problems in computer vision and image processing. In this paper, we investigate the application of CS paradigms on single image super-resolution (SR) problems that are considered to be the most challenging in this class. In light of recent promising results, we propose novel tools for analyzing sparse representation-based inverse problems using redundant dictionary basis. Further, we provide novel results establishing tighter correspondence between SR and CS. As such, we gain insights into questions concerning regularizing the solution to the underdetermined problem, such as follows. 1) Is sparsity prior alone sufficient? 2) What is a good dictionary? 3) What is the practical implication of noncompliance with theoretical CS hypothesis? Unlike in other underdetermined problems that assume random downprojections, the low-resolution image formation model employed in CS-based SR is a deterministic down-projection that may not necessarily satisfy some critical assumptions of CS. We further investigate the impact of such projections in concern to the above questions.

Super-resolution: a comprehensive survey

“…These algorithms [379] (2008), [380], [390], [486], [498], [503], [505], [517], [557], [571], [572], [576], [578], [579], [583], [595], [597], [601], [602], [604], [608], [614] usually assume that there are two overcomplete dictionaries: one for the HR patches, D h , and one for their corresponding LR counterparts, D l . The latter has been produced from the former by a degradation process like that in Eq.…”

Single image super-resolution using sparse representations with structure constraints

“…In [8], Kulkarni et al make a parallel between sparse representations using dictionaries and sparse representations using orthonormal bases. Experiments show that sparse representations is satisfied for several kinds of dictionaries, such as learned dictionaries and non-trained dictionary [8].…”

“…Experiments show that sparse representations is satisfied for several kinds of dictionaries, such as learned dictionaries and non-trained dictionary [8]. However, Kulkarani et al give evidences that trained dictionaries perform much better than non-trained dictionaries in terms of consistency for solutions, local patchwise discontinuities and performance.…”

“…when λ+ ≈ λ− ≈ 0) [18]. In order to detect salient edges, we use the function named as S-norm presented in Equation (8), where p = (x, y) represent the pixel coordinates.…”

Image Super Resolution Reconstruction Based MCA and PCA Dimension Reduction

“…On the basis of Yang proposed a new MCA [7] [8] based and dictionary learning [9] [10] of image super-resolution reconstruction algorithm, first MCA method is decomposed low-resolution image into structure and texture part, and then low-resolution texture image is trained the over-complete dictionary. Because of the complexity of texture images, so using super resolution reconstruction method based on sparse representation [11] [12]. In the feature extraction process of dictionary training phase using the method that combined with second derivative and gradient direction.…”