Truncated Nuclear Norm Minimization Based Group Sparse Representation for Image Restoration

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