Proximal Linearized Minimization Algorithm for Nonsmooth Nonconvex Minimization Problems in Image Deblurring with Impulse Noise  

作　　者：Shirong DENG Yuchao TANG 

机构地区：[1]School of Mathematics and Information Science,Guangzhou University,Guangdong 510006,P.R.China [2]Department of Mathematics,Nanchang University,Jiangxi 330031,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第1期122-142,共21页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundations of China(Grant No.12061045,12031003);the Guangzhou Education Scientific Research Project 2024(Grant No.202315829);the Natural Science Foundation of Jiangxi Province(Grant No.20224ACB211004)。

摘　　要：Impulse noise removal is an important task in image restoration.In this paper,we introduce a general nonsmooth nonconvex model for recovering images degraded by blur and impulsive noise,which can easily include some prior information,such as box constraint or low rank,etc.To deal with the nonconvex problem,we employ the proximal linearized minimization algorithm.For the subproblem,we use the alternating direction method of multipliers to solve it.Furthermore,based on the assumption that the objective function satisfies the KurdykaLojasiewicz property,we prove the global convergence of the proposed algorithm.Numerical experiments demonstrate that our method outperforms both the l1TV and Nonconvex TV models in terms of subjective and objective quality measurements.

关 键 词：nonconvex data fidelity term impulse noise total variation proximal linearized minimization 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TP18[自动化与计算机技术—计算机科学与技术]