Reconciliation of Group Sparsity and Low-rank models for Image Restoration

Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) or group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, i.e., JS enforces the sparse codes to share the same support, or too general, i.e., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches.
To make the proposed scheme tractable and robust, an alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem. Experimental results on both image deblocking and denoising demonstrate that the proposed LR-GSC image restoration algorithms outperform many popular or state-of-the-art methods, in terms of both the objective and perceptual quality.