Compressive Sensing (CS) theory shows that a signal can be decoded from many
fewer measurements than suggested by the Nyquist sampling theory, when the
signal is sparse in some domain. Most of conventional CS recovery approaches,
however, exploited a set of fixed bases (e.g. DCT, wavelet, contourlet and
gradient domain) for the entirety of a signal, which are irrespective of the
nonstationarity of natural signals and cannot achieve high enough degree of
sparsity, thus resulting in poor rate-distortion performance. In this paper, we
propose a new framework for image compressive sensing recovery via structural
group sparse representation (SGSR) modeling, which enforces image sparsity and
self-similarity simultaneously under a unified framework in an adaptive group
domain, thus greatly confining the CS solution space. In addition, an efficient
iterative shrinkage/thresholding algorithm based technique is developed to
solve the above optimization problem. Experimental results demonstrate that the
novel CS recovery strategy achieves significant performance improvements over
the current state-of-the-art schemes and exhibits nice convergence.

本论文提出了一种新的图像压缩感知恢复策略 —— 通过结构分组稀疏表示 (SGSR) 建模，在自适应的分组域中同时强制图像稀疏性和自相似性，并开发了一种高效的迭代收缩 / 阈值算法技术来解决上述优化问题。实验结果表明，这种新的压缩感知恢复策略相对于当前最先进的方案实现了显著的性能改进，并且表现出了不错的收敛性。

基于结构群稀疏表示的图像压缩感知恢复

Structural Group Sparse Representation for Image Compressive Sensing  Recovery

The problem of restoration of digital images from their degraded measurements
plays a central role in a multitude of practically important applications. A
particularly challenging instance of this problem occurs in the case when the
degradation phenomenon is modeled by an ill-conditioned operator. In such a
case, the presence of noise makes it impossible to recover a valuable
approximation of the image of interest without using some a priori information
about its properties. Such a priori information is essential for image
restoration, rendering it stable and robust to noise. Particularly, if the
original image is known to be a piecewise smooth function, one of the standard
priors used in this case is defined by the Rudin-Osher-Fatemi model, which
results in total variation (TV) based image restoration. The current arsenal of
algorithms for TV-based image restoration is vast. In the present paper, a
different approach to the solution of the problem is proposed based on the
method of iterative shrinkage (aka iterated thresholding). In the proposed
method, the TV-based image restoration is performed through a recursive
application of two simple procedures, viz. linear filtering and soft
thresholding. Therefore, the method can be identified as belonging to the group
of first-order algorithms which are efficient in dealing with images of
relatively large sizes. Another valuable feature of the proposed method
consists in its working directly with the TV functional, rather then with its
smoothed versions. Moreover, the method provides a single solution for both
isotropic and anisotropic definitions of the TV functional, thereby
establishing a useful connection between the two formulae.

提出了一种基于迭代收缩方法和 TV 功能的算法，可以高效地处理大型数字图像，实现从退化图像中恢复原始图像。