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。