Image Recovery based on Local and Nonlocal Regularizations

Recently, a nonlocal low-rank regularization based compressive sensing approach (NLR) which exploits structured sparsity of similar patches has shown the state-of-the-art performance in image recovery. However, NLR cannot efficiently preserve local structures because it ignores the relationship between pixels. In addition, the surrogate logdet function used in NLR cannot well approximate the rank. In this paper, a novel approach based on local and nonlocal regularizations toward exploiting the sparse-gradient property and nonlocal low-rank property (SGLR) has been proposed. Weighted schatten-p norm and l (q) norm have been used as better non-convex surrogate functions for the rank and l0 norm. In addition, an efficient iterative algorithm is developed to solve the resulting recovery problem. The experimental results have demonstrated that SGLR outperforms existing state-of-the-art CS algorithms.