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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":"45 7-9","pages":"411-440"},"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":"9 1","pages":""},"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 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":"28 1","pages":""},"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
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":"85 1","pages":""},"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
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":"89 1","pages":""},"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
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":"131 1","pages":""},"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
Domain Generalization by Functional Regression 通过函数回归实现领域泛化
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-03-04 DOI: 10.1080/01630563.2024.2320663
Markus Holzleitner, Sergei V. Pereverzyev, Werner Zellinger
{"title":"Domain Generalization by Functional Regression","authors":"Markus Holzleitner, Sergei V. Pereverzyev, Werner Zellinger","doi":"10.1080/01630563.2024.2320663","DOIUrl":"https://doi.org/10.1080/01630563.2024.2320663","url":null,"abstract":"The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen thr...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"232 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033909","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
Rates of Convergence and Metastability for Chidume’s Algorithm for the Approximation of Zeros of Accretive Operators in Banach Spaces 巴拿赫空间中可变算子零点逼近奇杜梅算法的收敛率和可转移性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-02-28 DOI: 10.1080/01630563.2024.2318597
Richard Findling, Ulrich Kohlenbach
{"title":"Rates of Convergence and Metastability for Chidume’s Algorithm for the Approximation of Zeros of Accretive Operators in Banach Spaces","authors":"Richard Findling, Ulrich Kohlenbach","doi":"10.1080/01630563.2024.2318597","DOIUrl":"https://doi.org/10.1080/01630563.2024.2318597","url":null,"abstract":"In this paper we give a quantitative analysis of an explicit iteration method due to C.E. Chidume for the approximation of a zero of an m-accretive operator A:X→2X in Banach spaces which does not i...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005088","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
Regularized Nyström Subsampling in Covariate Shift Domain Adaptation Problems 变量偏移域适应问题中的正则化尼斯特伦子采样
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-02-23 DOI: 10.1080/01630563.2024.2318572
Hanna L. Myleiko, Sergei G. Solodky
{"title":"Regularized Nyström Subsampling in Covariate Shift Domain Adaptation Problems","authors":"Hanna L. Myleiko, Sergei G. Solodky","doi":"10.1080/01630563.2024.2318572","DOIUrl":"https://doi.org/10.1080/01630563.2024.2318572","url":null,"abstract":"The unsupervised domain adaptation problem with covariate shift assumption is considered. Within the framework of the Reproducing Kernel Hilbert Space concept, an algorithm is constructed that is a...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139949651","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
Quadratic Neural Networks for Solving Inverse Problems 用于解决逆问题的二次元神经网络
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2024-02-22 DOI: 10.1080/01630563.2024.2316580
Leon Frischauf, Otmar Scherzer, Cong Shi
{"title":"Quadratic Neural Networks for Solving Inverse Problems","authors":"Leon Frischauf, Otmar Scherzer, Cong Shi","doi":"10.1080/01630563.2024.2316580","DOIUrl":"https://doi.org/10.1080/01630563.2024.2316580","url":null,"abstract":"In this paper we investigate the solution of inverse problems with neural network ansatz functions with generalized decision functions. The relevant observation for this work is that such functions...","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139949650","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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