On the Strong Convexity of PnP Regularization Using Linear Denoisers

IF 3.2 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Arghya Sinha;Kunal N. Chaudhury
{"title":"On the Strong Convexity of PnP Regularization Using Linear Denoisers","authors":"Arghya Sinha;Kunal N. Chaudhury","doi":"10.1109/LSP.2024.3475913","DOIUrl":null,"url":null,"abstract":"In the Plug-and-Play (PnP) method, a denoiser is used as a regularizer within classical proximal algorithms for image reconstruction. It is known that a broad class of linear denoisers can be expressed as the proximal operator of a convex regularizer. Consequently, the associated PnP algorithm can be linked to a convex optimization problem \n<inline-formula><tex-math>$\\mathcal {P}$</tex-math></inline-formula>\n. For such a linear denoiser, we prove that \n<inline-formula><tex-math>$\\mathcal {P}$</tex-math></inline-formula>\n exhibits strong convexity for linear inverse problems. Specifically, we show that the strong convexity of \n<inline-formula><tex-math>$\\mathcal {P}$</tex-math></inline-formula>\n can be used to certify objective and iterative convergence of \n<italic>any</i>\n PnP algorithm derived from classical proximal methods.","PeriodicalId":13154,"journal":{"name":"IEEE Signal Processing Letters","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Signal Processing Letters","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10706773/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0

Abstract

In the Plug-and-Play (PnP) method, a denoiser is used as a regularizer within classical proximal algorithms for image reconstruction. It is known that a broad class of linear denoisers can be expressed as the proximal operator of a convex regularizer. Consequently, the associated PnP algorithm can be linked to a convex optimization problem $\mathcal {P}$ . For such a linear denoiser, we prove that $\mathcal {P}$ exhibits strong convexity for linear inverse problems. Specifically, we show that the strong convexity of $\mathcal {P}$ can be used to certify objective and iterative convergence of any PnP algorithm derived from classical proximal methods.
论使用线性去oisers 的 PnP 正则化的强凸性
在即插即用(PnP)方法中,去噪器被用作图像重建经典近端算法中的正则化器。众所周知,一大类线性去噪器可以表示为凸正则的近似算子。因此,相关的 PnP 算法可以与凸优化问题 $\mathcal {P}$ 联系起来。对于这种线性去噪器,我们证明 $\mathcal {P}$ 对于线性逆问题具有强凸性。具体来说,我们证明了 $\mathcal {P}$ 的强凸性可以用来证明任何从经典近似方法衍生的 PnP 算法的目标和迭代收敛性。
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
IEEE Signal Processing Letters
IEEE Signal Processing Letters 工程技术-工程:电子与电气
CiteScore
7.40
自引率
12.80%
发文量
339
审稿时长
2.8 months
期刊介绍: The IEEE Signal Processing Letters is a monthly, archival publication designed to provide rapid dissemination of original, cutting-edge ideas and timely, significant contributions in signal, image, speech, language and audio processing. Papers published in the Letters can be presented within one year of their appearance in signal processing conferences such as ICASSP, GlobalSIP and ICIP, and also in several workshop organized by the Signal Processing Society.
×
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