  Nonlocal self-similarity and group sparsity have been widely utilized in
image compressive sensing (CS). However, when the sampling rate is low, the
internal prior information of degraded images may be not enough for accurate
restoration, resulting in loss of image edges and details. In this paper, we
propose a joint group and residual sparse coding method for CS image recovery
(JGRSC-CS). In the proposed JGRSC-CS, patch group is treated as the basic unit
of sparse coding and two dictionaries (namely internal and external
dictionaries) are applied to exploit the sparse representation of each group
simultaneously. The internal self-adaptive dictionary is used to remove
artifacts, and an external Gaussian Mixture Model (GMM) dictionary, learned
from clean training images, is used to enhance details and texture. To make the
proposed method effective and robust, the split Bregman method is adopted to
reconstruct the whole image. Experimental results manifest the proposed
JGRSC-CS algorithm outperforms existing state-of-the-art methods in both peak
signal to noise ratio (PSNR) and visual quality.
