Joint group and residual sparse coding for image compressive sensing

Nonlocal self-similarity and group sparsity have been widely utilized in image compressive sensing (CS). Most existing methods utilize either internal priors or external priors. However, when the sampling rate is low, the internal prior information of degraded images is not enough for accurate restoration, resulting in loss of image edges and details. And external prior, which learned from clean data, may be not adaptive to the images. 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. Different from the idea of encoding a group with a single dictionary (e.g. DCT, Curvelet or K-SVD dictionary), 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 that with acceptable computational complexity and good convergence property, the proposed JGRSC-CS algorithm outperforms existing state-of-the-art methods in both peak signal to noise ratio (PSNR) and visual quality. © 2020 Elsevier B.V.