Total variation regularized multi-matrices weighted Schatten p-norm minimization for image denoising

Abstract

Motivated by the superior performance of nonconvex nonsmooth Lp (0<p<1) norm, this paper introduces a novel method that combines the weighted Schatten p-norm, Lp-norm, and total variation regularization based on the multiple matrices denoising framework. The weighted Schatten p-norm encodes the global low-rank to multiple matrices data, while the Lp-norm provides noise robustness. Total variation regularization is incorporated to promote structural smoothness and edge preservation in the image. To solve the nonconvex and nonsmooth model, an efficient alternating direction method of multipliers (ADMM) is designed. In addition, we discuss how the value of p in the three items affects the denoising performance in simulated images. Extensive experiments on face datasets, videos, and real-world noisy images demonstrate that the proposed method significantly improves denoising performance, particularly for removing large sparse noise.