Low-Rankness Guided Group Sparse Representation for Image Restoration

As a spotlighted nonlocal image representation model, group sparse representation (GSR) has demonstrated a great potential in diverse image restoration tasks. Most of the existing GSR-based image restoration approaches exploit the nonlocal self-similarity (NSS) prior by clustering similar patches into groups and imposing sparsity to each group coefficient, which can effectively preserve image texture information. However, these methods have imposed only plain sparsity over each individual patch of the group, while neglecting other beneficial image properties, e.g., low-rankness (LR), leads to degraded image restoration results. In this article, we propose a novel low-rankness guided group sparse representation (LGSR) model for highly effective image restoration applications. The proposed LGSR jointly utilizes the sparsity and LR priors of each group of similar patches under a unified framework. The two priors serve as the complementary priors in LGSR for effectively preserving the texture and structure information of natural images. Moreover, we apply an alternating minimization algorithm with an adaptively adjusted parameter scheme to solve the proposed LGSR-based image restoration problem. Extensive experiments are conducted to demonstrate that the proposed LGSR achieves superior results compared with many popular or state-of-the-art algorithms in various image restoration tasks, including denoising, inpainting, and compressive sensing (CS).