Image Compressive Sensing Recovery Using Group Sparse Coding via Non-convex Weighted Lp Minimization

Compressive sensing (CS) has attracted considerable research from signal/image processing communities. Recent studies further show that structured or group sparsity often leads to more powerful signal reconstruction techniques in various CS taskes. Unlike the conventional sparsity-promoting convex regularization methods, this paper proposes a new approach for image compressive sensing recovery using group sparse coding via non-convex weighted $\ell_p$ minimization. To make our scheme tractable and robust, an iterative shrinkage/thresholding (IST) algorithm based technique is adopted to solve the above non-convex $\ell_p$ minimization problem efficiently. Experimental results have shown that the proposed algorithm outperforms many state-of-the-art techniques for image CS recovery.