RLGC: residual low rank group sparsity constraint for image denoising

Image denoising is an important topic in the field of image processing. With the application of nonlocal similarity in sparse representation, the work of image denoising began to be performed on similar patch groups. The sparse representations of patches in a group will be learned together. In this paper, we propose a novel image denoising model by combining group sparsity residual with low-rankness. Firstly, motivated by the relationship between low rank and sparsity, a low rank constraint is imposed on the sparse coefficient matrix of each similar patch group to enhance the sparsity. Secondly, since 𝛾-norm can most closely match the true rank of a matrix, it is applied for rank approximation in our model. Finally, in view of the fact that numerous iterations are required in the group sparse representation (GSR) model, we develop an efficient algorithm based on the Majorize-Minimization (MM) optimization. It greatly reduces the computational complexity and the number of iterations. Experimental results show that our model makes great improvements in image denoising and outperforms many state-of-the-art methods.