Denoising by low-rank and sparse representations

Due to the ill-posed nature of image denoising problem, good image priors are of great importance for an effective restoration. Nonlocal self-similarity and sparsity are two popular and widely used image priors which have led to several state-of-the-art methods in natural image denoising. In this paper, we take advantage of these priors and propose a new denoising algorithm based on sparse and low-rank representation of image patches under a nonlocal framework. This framework consists of two complementary steps. In the first step, noise removal from groups of matched image patches is formulated as recovery of low-rank matrices from noisy data. This problem is then efficiently solved under asymptotic matrix reconstruction model based on recent results from random matrix theory which leads to a parameter-free optimal estimator. Nonlocal learned sparse representation is adopted in the second step to suppress artifacts introduced in the previous estimate. Experimental results, demonstrate the superior denoising performance of the proposed algorithm as compared with the state-of-the-art methods.