A Combination Model for Image Denoising

作     者：Yi-ping XU 

作者机构：School of ScienceSouthwest University of Science and Technology 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2016年第32卷第3期

页      面：781-792页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 070104[理学-应用数学] 0802[工学-机械工程] 0701[理学-数学] 

基　　金：Supported by the Natural Science Foundation of Sichuan Provincial Department of Education(No.15ZB0110) 

主　　题：image denoising partial differential equations split Bregman method algebraic multi-grid method Krylov subspace acceleration 

摘      要：In this paper, we propose an efficient combination model of the second-order ROF model and a simple fourth-order partial differential equation （PDE） for image denoising. The split Bregman method is used to convert the nonlinear combination model into a linear system in the outer iteration, and an algebraic multigrid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. At the same time, we prove that the model is strictly convex and exists a unique global minimizer. We have also conducted a variety of numerical experiments to analyze the parameter selection criteria and discuss the performance of ~he fourth-order PDE in the combination model. The results show that our model can reduce blocky effects and our algorithm is efficient and robust to solve the proposed model.