Multi-band weighted [formula omitted] norm minimization for image denoising

Abstract

Low rank matrix approximation (LRMA) has a wide range of applications in computer vision and has drawn much attention in recent years. A typical nuclear norm minimization (NNM) is often used to solve a LRMA, but this is likely to overshrink the rank components due to having the same threshold. To address this problem, we propose a flexible and precise model named multi-band weighted lp norm minimization (MBWPNM). We have reformulated it into nonconvex lp norm subproblems under certain weight conditions, and we solve these subproblems via a generalized soft-thresholding algorithm. We then adopt MBWPNM for image (grayscale, color and multispectral) denoising. The proposed MBWPNM not only guarantees a more accurate approximation with a Schatten p-norm in case of a change of noise levels, but it also considers prior knowledge, for which different rank components have varying importance. Extensive experiments on additive white Gaussian noise removal and realistic noise removal demonstrate that the proposed MBWPNM achieves better performance than several state-of-the-art algorithms.