Image compressive sensing using group sparse representation via truncated nuclear norm minimization

Group sparse representation (GSR) has shown great potential in image Compressive Sensing (CS) recovery, which can be considered as a low rank matrix approximation problem. The nuclear norm minimization can only minimize all the singular values simultaneously. Recent advances have suggested the truncated nuclear norm minimization (TNNM) to better approximate the matrix rank. In this paper, we connect group sparse representation with truncated nuclear norm minimization for CS image recovery. Then, an implementation of fast convergence via the alternating direction method of multipliers (ADMM) is developed to solve the proposed problem. Moreover, an effective dictionary for each group is learned from the recovery image itself rather than a large number of natural image dataset. Experimental results demonstrate that the proposed GSR-TNNM method achieves a good convergence performance and is able to improve image CS recovery quality significantly compared with the state-of-the-art methods.