Feasibility-based fixed point networks

Abstract Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect to data perturbations. Hand-chosen...

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Autores principales:	Howard Heaton, Samy Wu Fung, Aviv Gibali, Wotao Yin
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Convex feasibility problem Projection Averaged Fixed point network Nonexpansive Learned regularizer Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/44f7425af370421a908ad4da0f3a81fc
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spelling	oai:doaj.org-article:44f7425af370421a908ad4da0f3a81fc2021-11-28T12:14:03ZFeasibility-based fixed point networks10.1186/s13663-021-00706-32730-5422https://doaj.org/article/44f7425af370421a908ad4da0f3a81fc2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13663-021-00706-3https://doaj.org/toc/2730-5422Abstract Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect to data perturbations. Hand-chosen analytic regularization can yield desirable theoretical guarantees, but such approaches have limited effectiveness recovering signals due to their inability to leverage large amounts of available data. To this end, this work fuses data-driven regularization and convex feasibility in a theoretically sound manner. This is accomplished using feasibility-based fixed point networks (F-FPNs). Each F-FPN defines a collection of nonexpansive operators, each of which is the composition of a projection-based operator and a data-driven regularization operator. Fixed point iteration is used to compute fixed points of these operators, and weights of the operators are tuned so that the fixed points closely represent available data. Numerical examples demonstrate performance increases by F-FPNs when compared to standard TV-based recovery methods for CT reconstruction and a comparable neural network based on algorithm unrolling. Codes are available on Github: github.com/howardheaton/feasibility_fixed_point_networks .Howard HeatonSamy Wu FungAviv GibaliWotao YinSpringerOpenarticleConvex feasibility problemProjectionAveragedFixed point networkNonexpansiveLearned regularizerApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Algorithms for Sciences and Engineering, Vol 2021, Iss 1, Pp 1-19 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Convex feasibility problem Projection Averaged Fixed point network Nonexpansive Learned regularizer Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Convex feasibility problem Projection Averaged Fixed point network Nonexpansive Learned regularizer Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Howard Heaton Samy Wu Fung Aviv Gibali Wotao Yin Feasibility-based fixed point networks
description	Abstract Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect to data perturbations. Hand-chosen analytic regularization can yield desirable theoretical guarantees, but such approaches have limited effectiveness recovering signals due to their inability to leverage large amounts of available data. To this end, this work fuses data-driven regularization and convex feasibility in a theoretically sound manner. This is accomplished using feasibility-based fixed point networks (F-FPNs). Each F-FPN defines a collection of nonexpansive operators, each of which is the composition of a projection-based operator and a data-driven regularization operator. Fixed point iteration is used to compute fixed points of these operators, and weights of the operators are tuned so that the fixed points closely represent available data. Numerical examples demonstrate performance increases by F-FPNs when compared to standard TV-based recovery methods for CT reconstruction and a comparable neural network based on algorithm unrolling. Codes are available on Github: github.com/howardheaton/feasibility_fixed_point_networks .
format	article
author	Howard Heaton Samy Wu Fung Aviv Gibali Wotao Yin
author_facet	Howard Heaton Samy Wu Fung Aviv Gibali Wotao Yin
author_sort	Howard Heaton
title	Feasibility-based fixed point networks
title_short	Feasibility-based fixed point networks
title_full	Feasibility-based fixed point networks
title_fullStr	Feasibility-based fixed point networks
title_full_unstemmed	Feasibility-based fixed point networks
title_sort	feasibility-based fixed point networks
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/44f7425af370421a908ad4da0f3a81fc
work_keys_str_mv	AT howardheaton feasibilitybasedfixedpointnetworks AT samywufung feasibilitybasedfixedpointnetworks AT avivgibali feasibilitybasedfixedpointnetworks AT wotaoyin feasibilitybasedfixedpointnetworks
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Feasibility-based fixed point networks

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