Sampling and reconstruction by means of weighted inverses

Autores
Arias, Maria Laura; Gonzalez, Maria Celeste
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, we address the problem of reconstructing an element in a Hilbert space from its samples by means of a weighted least square approximation. We show how this problem is linked with the notions of weighted inverses, weighted projections and an angle condition known as compatibility. In addition, we study perfect reconstruction operators and their relationship with the previous problem. Finally, since the reconstructions through these approaches may not be unique, we propose different criteria for choosing an optimal one among all of them.
Fil: Arias, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Gonzalez, Maria Celeste. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
SAMPLING PROBLEMS
PERFECT RECONSTRUCTIONS
WEIGHTED INVERSES
Nivel de accesibilidad
acceso embargado
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:11336/108158
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/108158
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Sampling and reconstruction by means of weighted inversesArias, Maria LauraGonzalez, Maria CelesteSAMPLING PROBLEMSPERFECT RECONSTRUCTIONSWEIGHTED INVERSEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article, we address the problem of reconstructing an element in a Hilbert space from its samples by means of a weighted least square approximation. We show how this problem is linked with the notions of weighted inverses, weighted projections and an angle condition known as compatibility. In addition, we study perfect reconstruction operators and their relationship with the previous problem. Finally, since the reconstructions through these approaches may not be unique, we propose different criteria for choosing an optimal one among all of them.Fil: Arias, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Gonzalez, Maria Celeste. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaSpringer2020-06info:eu-repo/date/embargoEnd/2020-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/108158Arias, Maria Laura; Gonzalez, Maria Celeste; Sampling and reconstruction by means of weighted inverses; Springer; Journal Of Fourier Analysis And Applications; 26; 3; 6-2020; 1-261069-58691531-5851CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00041-020-09747-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-020-09747-5info:eu-repo/semantics/embargoedAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:24:46Zoai:ri.conicet.gov.ar:11336/108158instacron: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:34982025-10-15 15:24:46.394CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sampling and reconstruction by means of weighted inverses
title Sampling and reconstruction by means of weighted inverses
spellingShingle Sampling and reconstruction by means of weighted inverses
Arias, Maria Laura
SAMPLING PROBLEMS
PERFECT RECONSTRUCTIONS
WEIGHTED INVERSES
title_short Sampling and reconstruction by means of weighted inverses
title_full Sampling and reconstruction by means of weighted inverses
title_fullStr Sampling and reconstruction by means of weighted inverses
title_full_unstemmed Sampling and reconstruction by means of weighted inverses
title_sort Sampling and reconstruction by means of weighted inverses
dc.creator.none.fl_str_mv Arias, Maria Laura
Gonzalez, Maria Celeste
author Arias, Maria Laura
author_facet Arias, Maria Laura
Gonzalez, Maria Celeste
author_role author
author2 Gonzalez, Maria Celeste
author2_role author
dc.subject.none.fl_str_mv SAMPLING PROBLEMS
PERFECT RECONSTRUCTIONS
WEIGHTED INVERSES
topic SAMPLING PROBLEMS
PERFECT RECONSTRUCTIONS
WEIGHTED INVERSES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article, we address the problem of reconstructing an element in a Hilbert space from its samples by means of a weighted least square approximation. We show how this problem is linked with the notions of weighted inverses, weighted projections and an angle condition known as compatibility. In addition, we study perfect reconstruction operators and their relationship with the previous problem. Finally, since the reconstructions through these approaches may not be unique, we propose different criteria for choosing an optimal one among all of them.
Fil: Arias, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Gonzalez, Maria Celeste. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description In this article, we address the problem of reconstructing an element in a Hilbert space from its samples by means of a weighted least square approximation. We show how this problem is linked with the notions of weighted inverses, weighted projections and an angle condition known as compatibility. In addition, we study perfect reconstruction operators and their relationship with the previous problem. Finally, since the reconstructions through these approaches may not be unique, we propose different criteria for choosing an optimal one among all of them.
publishDate 2020
dc.date.none.fl_str_mv 2020-06
info:eu-repo/date/embargoEnd/2020-12-01
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/11336/108158
Arias, Maria Laura; Gonzalez, Maria Celeste; Sampling and reconstruction by means of weighted inverses; Springer; Journal Of Fourier Analysis And Applications; 26; 3; 6-2020; 1-26
1069-5869
1531-5851
CONICET Digital
CONICET
url http://hdl.handle.net/11336/108158
identifier_str_mv Arias, Maria Laura; Gonzalez, Maria Celeste; Sampling and reconstruction by means of weighted inverses; Springer; Journal Of Fourier Analysis And Applications; 26; 3; 6-2020; 1-26
1069-5869
1531-5851
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00041-020-09747-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-020-09747-5
dc.rights.none.fl_str_mv info:eu-repo/semantics/embargoedAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv embargoedAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.22299

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