Anisotropic BV–L2 regularization of linear inverse ill-posed problems

Autores
Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Spies, Ruben Daniel
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
During the last two decades several generalizations of the traditional Tikhonov-Phillips regularization method for solving inverse ill-posed problems have been proposed. Many of these variants consist essentially of modifications on the penalizing term, which force certain features in the obtained regularized solution ([11,18]). If it is known that the regularity of the exact solution is inhomogeneous it is often desirable the use of mixed, spatially adaptive methods ([7,12]). These methods are also highly suitable when the preservation of edges is an important issue, since they allow for the inclusion of anisotropic penalizers for border detection ([20]). In this work we propose the use of a penalizer resulting from the convex spatially-adaptive combination of a classic L2penalizer and an anisotropic bounded variation seminorm. Results on existence and uniqueness of minimizers of the corresponding Tikhonov-Phillips functional are presented. Results on the stability of those minimizers with respect to perturbations in the data, in the regularization parameter and in the operator are also established. Applications to image restoration problems are shown.
Fil: Mazzieri, Gisela Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Temperini, Karina Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
Anisotropy
Bounded Variation
Inverse Problems
Tikhonov&Ndash;Phillips
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/63501
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Anisotropic BV–L2 regularization of linear inverse ill-posed problemsMazzieri, Gisela LucianaTemperini, Karina GuadalupeSpies, Ruben DanielAnisotropyBounded VariationInverse ProblemsTikhonov&Ndash;Phillipshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1During the last two decades several generalizations of the traditional Tikhonov-Phillips regularization method for solving inverse ill-posed problems have been proposed. Many of these variants consist essentially of modifications on the penalizing term, which force certain features in the obtained regularized solution ([11,18]). If it is known that the regularity of the exact solution is inhomogeneous it is often desirable the use of mixed, spatially adaptive methods ([7,12]). These methods are also highly suitable when the preservation of edges is an important issue, since they allow for the inclusion of anisotropic penalizers for border detection ([20]). In this work we propose the use of a penalizer resulting from the convex spatially-adaptive combination of a classic L2penalizer and an anisotropic bounded variation seminorm. Results on existence and uniqueness of minimizers of the corresponding Tikhonov-Phillips functional are presented. Results on the stability of those minimizers with respect to perturbations in the data, in the regularization parameter and in the operator are also established. Applications to image restoration problems are shown.Fil: Mazzieri, Gisela Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Temperini, Karina Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaAcademic Press Inc Elsevier Science2017-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/63501Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Spies, Ruben Daniel; Anisotropic BV–L2 regularization of linear inverse ill-posed problems; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 450; 1; 6-2017; 427-4430022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2017.01.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:05:39Zoai:ri.conicet.gov.ar:11336/63501instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:05:39.735CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Anisotropic BV–L2 regularization of linear inverse ill-posed problems
title Anisotropic BV–L2 regularization of linear inverse ill-posed problems
spellingShingle Anisotropic BV–L2 regularization of linear inverse ill-posed problems
Mazzieri, Gisela Luciana
Anisotropy
Bounded Variation
Inverse Problems
Tikhonov&Ndash;Phillips
title_short Anisotropic BV–L2 regularization of linear inverse ill-posed problems
title_full Anisotropic BV–L2 regularization of linear inverse ill-posed problems
title_fullStr Anisotropic BV–L2 regularization of linear inverse ill-posed problems
title_full_unstemmed Anisotropic BV–L2 regularization of linear inverse ill-posed problems
title_sort Anisotropic BV–L2 regularization of linear inverse ill-posed problems
dc.creator.none.fl_str_mv Mazzieri, Gisela Luciana
Temperini, Karina Guadalupe
Spies, Ruben Daniel
author Mazzieri, Gisela Luciana
author_facet Mazzieri, Gisela Luciana
Temperini, Karina Guadalupe
Spies, Ruben Daniel
author_role author
author2 Temperini, Karina Guadalupe
Spies, Ruben Daniel
author2_role author
author
dc.subject.none.fl_str_mv Anisotropy
Bounded Variation
Inverse Problems
Tikhonov&Ndash;Phillips
topic Anisotropy
Bounded Variation
Inverse Problems
Tikhonov&Ndash;Phillips
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv During the last two decades several generalizations of the traditional Tikhonov-Phillips regularization method for solving inverse ill-posed problems have been proposed. Many of these variants consist essentially of modifications on the penalizing term, which force certain features in the obtained regularized solution ([11,18]). If it is known that the regularity of the exact solution is inhomogeneous it is often desirable the use of mixed, spatially adaptive methods ([7,12]). These methods are also highly suitable when the preservation of edges is an important issue, since they allow for the inclusion of anisotropic penalizers for border detection ([20]). In this work we propose the use of a penalizer resulting from the convex spatially-adaptive combination of a classic L2penalizer and an anisotropic bounded variation seminorm. Results on existence and uniqueness of minimizers of the corresponding Tikhonov-Phillips functional are presented. Results on the stability of those minimizers with respect to perturbations in the data, in the regularization parameter and in the operator are also established. Applications to image restoration problems are shown.
Fil: Mazzieri, Gisela Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Temperini, Karina Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description During the last two decades several generalizations of the traditional Tikhonov-Phillips regularization method for solving inverse ill-posed problems have been proposed. Many of these variants consist essentially of modifications on the penalizing term, which force certain features in the obtained regularized solution ([11,18]). If it is known that the regularity of the exact solution is inhomogeneous it is often desirable the use of mixed, spatially adaptive methods ([7,12]). These methods are also highly suitable when the preservation of edges is an important issue, since they allow for the inclusion of anisotropic penalizers for border detection ([20]). In this work we propose the use of a penalizer resulting from the convex spatially-adaptive combination of a classic L2penalizer and an anisotropic bounded variation seminorm. Results on existence and uniqueness of minimizers of the corresponding Tikhonov-Phillips functional are presented. Results on the stability of those minimizers with respect to perturbations in the data, in the regularization parameter and in the operator are also established. Applications to image restoration problems are shown.
publishDate 2017
dc.date.none.fl_str_mv 2017-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/63501
Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Spies, Ruben Daniel; Anisotropic BV–L2 regularization of linear inverse ill-posed problems; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 450; 1; 6-2017; 427-443
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63501
identifier_str_mv Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Spies, Ruben Daniel; Anisotropic BV–L2 regularization of linear inverse ill-posed problems; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 450; 1; 6-2017; 427-443
0022-247X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2017.01.005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.993085

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