Procrustes problems and Parseval quasi-dual frames

Autores
Corach, Gustavo; Massey, Pedro Gustavo; Ruiz, Mariano Andres
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames F and X with synthesis operators F and X, the operator norm of FX∗−I measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with X and synthesized with F . Hence, for any given frame F , we compute explicitly the infimum of the operator norm of FX∗−I, where X is any Parseval frame. The X ’s that minimize this quantity are called Parseval quasi-dual frames of F . Our treatment considers both finite and infinite Parseval quasi-dual frames.
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Materia
Procrustes problems
Parseval frames
Dual frames
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:11336/12166
Acceder
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spelling Procrustes problems and Parseval quasi-dual framesCorach, GustavoMassey, Pedro GustavoRuiz, Mariano AndresProcrustes problemsParseval framesDual frameshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames F and X with synthesis operators F and X, the operator norm of FX∗−I measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with X and synthesized with F . Hence, for any given frame F , we compute explicitly the infimum of the operator norm of FX∗−I, where X is any Parseval frame. The X ’s that minimize this quantity are called Parseval quasi-dual frames of F . Our treatment considers both finite and infinite Parseval quasi-dual frames.Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaFil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaFil: Ruiz, Mariano Andres. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaSpringer2014-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/12166Corach, Gustavo; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Procrustes problems and Parseval quasi-dual frames; Springer; Acta Applicandae Mathematicae; 131; 1; 6-2014; 179-1950167-8019enginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10440-013-9853-0info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1309.7914info:eu-repo/semantics/altIdentifier/doi/10.1007/s10440-013-9853-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:55:49Zoai:ri.conicet.gov.ar:11336/12166instacron: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:34982025-11-12 09:55:49.741CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Procrustes problems and Parseval quasi-dual frames
title Procrustes problems and Parseval quasi-dual frames
spellingShingle Procrustes problems and Parseval quasi-dual frames
Corach, Gustavo
Procrustes problems
Parseval frames
Dual frames
title_short Procrustes problems and Parseval quasi-dual frames
title_full Procrustes problems and Parseval quasi-dual frames
title_fullStr Procrustes problems and Parseval quasi-dual frames
title_full_unstemmed Procrustes problems and Parseval quasi-dual frames
title_sort Procrustes problems and Parseval quasi-dual frames
dc.creator.none.fl_str_mv Corach, Gustavo
Massey, Pedro Gustavo
Ruiz, Mariano Andres
author Corach, Gustavo
author_facet Corach, Gustavo
Massey, Pedro Gustavo
Ruiz, Mariano Andres
author_role author
author2 Massey, Pedro Gustavo
Ruiz, Mariano Andres
author2_role author
author
dc.subject.none.fl_str_mv Procrustes problems
Parseval frames
Dual frames
topic Procrustes problems
Parseval frames
Dual frames
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames F and X with synthesis operators F and X, the operator norm of FX∗−I measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with X and synthesized with F . Hence, for any given frame F , we compute explicitly the infimum of the operator norm of FX∗−I, where X is any Parseval frame. The X ’s that minimize this quantity are called Parseval quasi-dual frames of F . Our treatment considers both finite and infinite Parseval quasi-dual frames.
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
description Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames F and X with synthesis operators F and X, the operator norm of FX∗−I measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with X and synthesized with F . Hence, for any given frame F , we compute explicitly the infimum of the operator norm of FX∗−I, where X is any Parseval frame. The X ’s that minimize this quantity are called Parseval quasi-dual frames of F . Our treatment considers both finite and infinite Parseval quasi-dual frames.
publishDate 2014
dc.date.none.fl_str_mv 2014-06
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/11336/12166
Corach, Gustavo; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Procrustes problems and Parseval quasi-dual frames; Springer; Acta Applicandae Mathematicae; 131; 1; 6-2014; 179-195
0167-8019
url http://hdl.handle.net/11336/12166
identifier_str_mv Corach, Gustavo; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Procrustes problems and Parseval quasi-dual frames; Springer; Acta Applicandae Mathematicae; 131; 1; 6-2014; 179-195
0167-8019
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/article/10.1007/s10440-013-9853-0
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1309.7914
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10440-013-9853-0
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/zip
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 13.25334

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