Computer Science

CLC number: TP 751

Group Sparsity Residual Constraint Image Denoising Model with 𝒍₁/𝒍₂ Regularization

¹ Key Laboratory of Multidisciplinary Management and Control of Complex Systems of Anhui Higher Education Institutes, Anhui University of Technology, Maanshan 243002, Anhui, China
² School of Mathematics and Physics, Anhui University of Technology, Maanshan 243032, Anhui, China

^† To whom correspondence should be addressed. E-mail: zt9877@163.com

Received: 18 October 2022

Abstract

Group sparse residual constraint with non-local priors (GSRC) has achieved great success in image restoration producing state-of-the-art performance. In the GSRC model, the $l_{\mathrm{1}}$ norm minimization is employed to reduce the group sparse residual. In recent years, non-convex regularization terms have been widely used in image denoising problems, which have achieved better results in denoising than convex regularization terms. In this paper, we use the ratio of the $l_{\mathrm{1}}$ and $l_{\mathrm{2}}$ norm instead of the $l_{\mathrm{1}}$ norm to propose a new image denoising model, i.e., a group sparse residual constraint model with $l_{\mathrm{1}}/l_{\mathrm{2}}$ minimization (GSRC-$l_{\mathrm{1}}/l_{\mathrm{2}}$). Due to the computational difficulties arisen from the non-convexity and non-linearity, we focus on a constrained optimization problem that can be solved by alternative direction method of multipliers (ADMM). Experimental results of image denoising show that the pro-posed model outperforms several state-of-the-art image denoising methods both visually and quantitatively.