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Iteratively Refined Image Reconstruction with Learned Attentive Regularizers. 利用学习型注意正则迭代精炼图像重构
IF 1.4 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-08-11 eCollection Date: 2024-01-01 DOI: 10.1080/01630563.2024.2384849
Mehrsa Pourya, Sebastian Neumayer, Michael Unser
{"title":"Iteratively Refined Image Reconstruction with Learned Attentive Regularizers.","authors":"Mehrsa Pourya, Sebastian Neumayer, Michael Unser","doi":"10.1080/01630563.2024.2384849","DOIUrl":"10.1080/01630563.2024.2384849","url":null,"abstract":"<p><p>We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In contrast, our scheme is interpretable because it corresponds to the minimization of a series of convex problems. For each problem in the series, a mask is generated based on the previous solution to refine the regularization strength spatially. In this way, the model becomes progressively attentive to the image structure. For the underlying update operator, we prove the existence of a fixed point. As a special case, we investigate a mask generator for which the fixed-point iterations converge to a critical point of an explicit energy functional. In our experiments, we match the performance of state-of-the-art learned variational models for the solution of inverse problems. Additionally, we offer a promising balance between interpretability, theoretical guarantees, reliability, and performance.</p>","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11371266/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142134481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Type of Ill-Posedness of Generalized Hilbert Matrices and Related Operators 论广义希尔伯特矩阵及相关算子的问题类型
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-08-11 DOI: 10.1080/01630563.2024.2384869
Stefan Kindermann
{"title":"On the Type of Ill-Posedness of Generalized Hilbert Matrices and Related Operators","authors":"Stefan Kindermann","doi":"10.1080/01630563.2024.2384869","DOIUrl":"https://doi.org/10.1080/01630563.2024.2384869","url":null,"abstract":"We consider infinite-dimensional generalized Hilbert matrices of the form Hi,j=didjxi+xj, where di are nonnegative weights and xi are pairwise distinct positive numbers. We state sufficient and, fo...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some generalizations of Darbo- and Sadovskii- type fixed point theorems in Fréchet spaces 关于弗雷谢特空间中达尔博型和萨多夫斯基型定点定理的一些概论
IF 1.4 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-08-09 DOI: 10.1080/01630563.2024.2384860
L. Olszowy, Tomasz Zając
{"title":"On some generalizations of Darbo- and Sadovskii- type fixed point theorems in Fréchet spaces","authors":"L. Olszowy, Tomasz Zając","doi":"10.1080/01630563.2024.2384860","DOIUrl":"https://doi.org/10.1080/01630563.2024.2384860","url":null,"abstract":"","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141922511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stabilized SQP Methods in Hilbert Spaces 希尔伯特空间中的稳定 SQP 方法
IF 1.4 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-08-09 DOI: 10.1080/01630563.2024.2384861
Andrian Uihlein, W. Wollner
{"title":"Stabilized SQP Methods in Hilbert Spaces","authors":"Andrian Uihlein, W. Wollner","doi":"10.1080/01630563.2024.2384861","DOIUrl":"https://doi.org/10.1080/01630563.2024.2384861","url":null,"abstract":"","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141922166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Bregman-proximal iterative algorithm for the monotone inclusion problem in Banach spaces 论巴拿赫空间中单调包含问题的布雷格曼-近似迭代算法
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-05-29 DOI: 10.1080/01630563.2024.2349006
Yan Tang, Shiqing Zhang, Yeol Je Cho
{"title":"On the Bregman-proximal iterative algorithm for the monotone inclusion problem in Banach spaces","authors":"Yan Tang, Shiqing Zhang, Yeol Je Cho","doi":"10.1080/01630563.2024.2349006","DOIUrl":"https://doi.org/10.1080/01630563.2024.2349006","url":null,"abstract":"In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximal point it...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frames and Dual Frames for Krein Spaces 克雷因空间的框架和双框架
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-05-20 DOI: 10.1080/01630563.2024.2349002
Yun-Zhang Li, Rui-Qi Dong
{"title":"Frames and Dual Frames for Krein Spaces","authors":"Yun-Zhang Li, Rui-Qi Dong","doi":"10.1080/01630563.2024.2349002","DOIUrl":"https://doi.org/10.1080/01630563.2024.2349002","url":null,"abstract":"","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141121390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix Transformation and Compactness on q -Catalan Sequence Spaces q -卡塔伦序列空间上的矩阵变换与紧凑性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-05-09 DOI: 10.1080/01630563.2024.2349003
Taja Yaying, F. Başar
{"title":"Matrix Transformation and Compactness on\u0000 q\u0000 -Catalan Sequence Spaces","authors":"Taja Yaying, F. Başar","doi":"10.1080/01630563.2024.2349003","DOIUrl":"https://doi.org/10.1080/01630563.2024.2349003","url":null,"abstract":"","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Dai-Liao Conjugate Gradient Method based on Approximately Optimal Stepsize for Unconstrained Optimization 基于无约束优化的近似最优步长的新岱廖梯度共轭法
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-04-02 DOI: 10.1080/01630563.2024.2333255
Yan Ni, Liu Zexian
{"title":"A New Dai-Liao Conjugate Gradient Method based on Approximately Optimal Stepsize for Unconstrained Optimization","authors":"Yan Ni, Liu Zexian","doi":"10.1080/01630563.2024.2333255","DOIUrl":"https://doi.org/10.1080/01630563.2024.2333255","url":null,"abstract":"Conjugate gradient methods are a class of very effective iterative methods for large-scale unconstrained optimization. In this paper, a new Dai-Liao conjugate gradient method for solving large-scal...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140580246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Motzkin Sequence Spaces and Motzkin Core 莫兹金序列空间和莫兹金核心
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-04-02 DOI: 10.1080/01630563.2024.2333250
Sezer Erdem, Serkan Demiriz, Adem Şahin
{"title":"Motzkin Sequence Spaces and Motzkin Core","authors":"Sezer Erdem, Serkan Demiriz, Adem Şahin","doi":"10.1080/01630563.2024.2333250","DOIUrl":"https://doi.org/10.1080/01630563.2024.2333250","url":null,"abstract":"In the current work, it is constructed the Motzkin matrix obtained by using Motzkin numbers M=(mrs) and is examined the sequence spaces c(M) and c0(M) described as the domain of Motzkin matrix M...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140579813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Diferential Inclusions Arising from Some Discontinuous Systems 论某些不连续系统产生的差分夹杂物
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-04-02 DOI: 10.1080/01630563.2024.2333251
A. V. Fominyh
{"title":"On Diferential Inclusions Arising from Some Discontinuous Systems","authors":"A. V. Fominyh","doi":"10.1080/01630563.2024.2333251","DOIUrl":"https://doi.org/10.1080/01630563.2024.2333251","url":null,"abstract":"The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140579714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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