Multi-Matrices Low-Rank Decomposition With Structural Smoothness for Image Denoising

Abstract

In this paper, we propose a multi-matrices low-rank decomposition method for image denoising. In this new method, the total variation (TV) norm is incorporated into low-rank approximation analysis to achieve structural smoothness and to improve quality of the recovered images. Our proposed mathematical framework for multi-matrices low-rank decomposition combines the nuclear norm, TV norm, and $\mathcal {L}_{1}$ norm, which allows us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Based on the iterative alternating direction method, we develop an algorithm to solve the proposed challenging optimization problem. We conduct extensive experiments and perform evaluations on multi-images denoising and multi-frames video prediction. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for images with large sparse noise.