Image Denoising Using Low Rank Matrix Approximation in Singular Value Decomposition

Abstract

The factorization of a matrix into lower rank matrices give solutions to a wide range of computer vision and image processing tasks. The inherent patches or the atomic patches can completely describe the whole image. The lower rank matrices are obtained using different tools including Singular Value Decomposition (SVD), which is typically found in minimization problems of nuclear norms. The singular values obtained will generally be a thresholder to realize the nuclear norm minimization. However, soft-thresholding is performed uniformly on all the singular values that lead to a similar importance to all the patches whether it is principal/useful or not. Our observation is that the decision on a patch (to be principal/useful or not) can be taken only when the application of this minimization is taken into consideration. Thus, in this paper, we propose a new method for image denoising by choosing variable weights to different singular values with a deep noise effect. Experimental results illustrate that the proposed weighted scheme performs better than the state-of-the-art methods.