Low-Rank Regularized Joint Sparsity For Image Denoising

Nonlocal sparse representation models such as group sparse representation (GSR), low-rankness and joint sparsity (JS) have shown great potentials in image denoising studies, by effectively exploiting image nonlocal self-similarity (NSS) property. Popular dictionary-based JS algorithms apply convex JS penalties in their objective functions, which avoid NP-hard sparse coding step, but lead to only approximately sparse representation. Such approximated JS models fail to impose low-rankness of the underlying image data, resulting in degraded quality in image restoration. To simultaneously exploit the low-rank and JS priors, we propose a novel low-rank regularized joint sparsity model, dubbed LRJS, to enhance the dependency (i.e., low-rankness) of similar patches, thus better suppress independent noise. Moreover, to make the optimization tractable and robust, an alternating minimization algorithm with an adaptive parameter adjustment strategy is developed to solve the proposed LRJS-based image denoising problem. Experimental results demonstrate that the proposed LRJS outperforms many popular or state-of-the-art denoising algorithms in terms of both objective and visual perception metrics.