Preconditioned Douglas-Rachford type primal-dual method for solving composite monotone inclusion problems with applications

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Yixuan Yang, Yuchao Tang, Meng Wen, T. Zeng
{"title":"Preconditioned Douglas-Rachford type primal-dual method for solving composite monotone inclusion problems with applications","authors":"Yixuan Yang, Yuchao Tang, Meng Wen, T. Zeng","doi":"10.3934/IPI.2021014","DOIUrl":null,"url":null,"abstract":"This paper is concerned with the monotone inclusion involving the sum of a finite number of maximally monotone operators and the parallel sum of two maximally monotone operators with bounded linear operators. To solve this monotone inclusion, we first transform it into the formulation of the sum of three maximally monotone operators in a proper product space. Then we derive two efficient iterative algorithms, which combine the partial inverse method with the preconditioned Douglas-Rachford splitting algorithm and the preconditioned proximal point algorithm. Furthermore, we develop an iterative algorithm, which relies on the preconditioned Douglas-Rachford splitting algorithm without using the partial inverse method. We carefully analyze the theoretical convergence of the proposed algorithms. Finally, in order to demonstrate the effectiveness and efficiency of these algorithms, we conduct numerical experiments on a novel image denoising model for salt-and-pepper noise removal. Numerical results show the good performance of the proposed algorithms.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"60 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems and Imaging","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/IPI.2021014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 5

Abstract

This paper is concerned with the monotone inclusion involving the sum of a finite number of maximally monotone operators and the parallel sum of two maximally monotone operators with bounded linear operators. To solve this monotone inclusion, we first transform it into the formulation of the sum of three maximally monotone operators in a proper product space. Then we derive two efficient iterative algorithms, which combine the partial inverse method with the preconditioned Douglas-Rachford splitting algorithm and the preconditioned proximal point algorithm. Furthermore, we develop an iterative algorithm, which relies on the preconditioned Douglas-Rachford splitting algorithm without using the partial inverse method. We carefully analyze the theoretical convergence of the proposed algorithms. Finally, in order to demonstrate the effectiveness and efficiency of these algorithms, we conduct numerical experiments on a novel image denoising model for salt-and-pepper noise removal. Numerical results show the good performance of the proposed algorithms.
求解复合单调包含问题的预条件Douglas-Rachford型原对偶方法及其应用
研究了有限个极大单调算子和两个极大单调算子与有界线性算子的平行和的单调包含。为了求解这个单调包含,我们首先将其转化为适当积空间中三个极大单调算子的和的表达式。然后推导了两种有效的迭代算法,将部分逆法与预条件Douglas-Rachford分裂算法和预条件近点算法相结合。此外,我们开发了一种迭代算法,该算法依赖于预条件的Douglas-Rachford分裂算法,而不使用部分逆方法。我们仔细分析了所提出算法的理论收敛性。最后,为了验证这些算法的有效性和效率,我们对一种新的图像去噪模型进行了数值实验,用于去除椒盐噪声。数值结果表明了所提算法的良好性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Inverse Problems and Imaging
Inverse Problems and Imaging 数学-物理:数学物理
CiteScore
2.50
自引率
0.00%
发文量
55
审稿时长
>12 weeks
期刊介绍: Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信