Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization

Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity, neglecting the relationship among similar patches. In this paper, a group-based sparse representation method with non-convex regularization (GSR-NCR) for image CS reconstruction is proposed. In GSR-NCR, the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework. Different from the previous methods based on sparsity-promoting convex regularization, we extend the non-convex weighted ℓp (0 < p < 1) penalty function on group sparse coefficients of the data matrix, rather than conventional ℓ1-based regularization. To reduce the computational complexity, instead of learning the dictionary with a high computational complexity from natural images, we learn the principle component analysis (PCA) based dictionary for each group. Moreover, to make the proposed scheme tractable and robust, we have developed an efficient iterative shrinkage/thresholding algorithm to solve the non-convex optimization problem. Experimental results demonstrate that the proposed method outperforms many state-of-the-art techniques for image CS reconstruction.