  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.
