Robust dual reconstruction systems and fusion frames

Autores
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the duality of reconstruction systems, which are g-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are particularly interested in the projective reconstruction systems that are the analogue of fusion frames in this context. Thus, we focus on dual systems of a fixed projective system that are optimal with respect to erasures of the reconstruction system coefficients involved in the decoding process. We consider two different measures of the reconstruction error in a blind reconstruction algorithm. We also study the projective reconstruction system that best approximate an arbitrary reconstruction system, based on some well known results in matrix theory. Finally, we present a family of examples in which the problem of existence of a dual projective system of a reconstruction system of this type is considered.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
DUAL RECONSTRUCTION SYSTEMS
ERASURES
FUSION FRAMES
RECONSTRUCTION SYSTEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/100310
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/100310
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Robust dual reconstruction systems and fusion framesMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioDUAL RECONSTRUCTION SYSTEMSERASURESFUSION FRAMESRECONSTRUCTION SYSTEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the duality of reconstruction systems, which are g-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are particularly interested in the projective reconstruction systems that are the analogue of fusion frames in this context. Thus, we focus on dual systems of a fixed projective system that are optimal with respect to erasures of the reconstruction system coefficients involved in the decoding process. We consider two different measures of the reconstruction error in a blind reconstruction algorithm. We also study the projective reconstruction system that best approximate an arbitrary reconstruction system, based on some well known results in matrix theory. Finally, we present a family of examples in which the problem of existence of a dual projective system of a reconstruction system of this type is considered.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaSpringer2012-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/100310Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Robust dual reconstruction systems and fusion frames; Springer; Acta Applicandae Mathematicae; 119; 1; 6-2012; 167-1830167-80191572-9036CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10440-011-9667-xinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1112.1654info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10440-011-9667-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:36:26Zoai:ri.conicet.gov.ar:11336/100310instacron: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:34982025-11-05 09:36:27.267CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Robust dual reconstruction systems and fusion frames
title Robust dual reconstruction systems and fusion frames
spellingShingle Robust dual reconstruction systems and fusion frames
Massey, Pedro Gustavo
DUAL RECONSTRUCTION SYSTEMS
ERASURES
FUSION FRAMES
RECONSTRUCTION SYSTEMS
title_short Robust dual reconstruction systems and fusion frames
title_full Robust dual reconstruction systems and fusion frames
title_fullStr Robust dual reconstruction systems and fusion frames
title_full_unstemmed Robust dual reconstruction systems and fusion frames
title_sort Robust dual reconstruction systems and fusion frames
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author_role author
author2 Ruiz, Mariano Andres
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv DUAL RECONSTRUCTION SYSTEMS
ERASURES
FUSION FRAMES
RECONSTRUCTION SYSTEMS
topic DUAL RECONSTRUCTION SYSTEMS
ERASURES
FUSION FRAMES
RECONSTRUCTION SYSTEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the duality of reconstruction systems, which are g-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are particularly interested in the projective reconstruction systems that are the analogue of fusion frames in this context. Thus, we focus on dual systems of a fixed projective system that are optimal with respect to erasures of the reconstruction system coefficients involved in the decoding process. We consider two different measures of the reconstruction error in a blind reconstruction algorithm. We also study the projective reconstruction system that best approximate an arbitrary reconstruction system, based on some well known results in matrix theory. Finally, we present a family of examples in which the problem of existence of a dual projective system of a reconstruction system of this type is considered.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We study the duality of reconstruction systems, which are g-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are particularly interested in the projective reconstruction systems that are the analogue of fusion frames in this context. Thus, we focus on dual systems of a fixed projective system that are optimal with respect to erasures of the reconstruction system coefficients involved in the decoding process. We consider two different measures of the reconstruction error in a blind reconstruction algorithm. We also study the projective reconstruction system that best approximate an arbitrary reconstruction system, based on some well known results in matrix theory. Finally, we present a family of examples in which the problem of existence of a dual projective system of a reconstruction system of this type is considered.
publishDate 2012
dc.date.none.fl_str_mv 2012-06
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/11336/100310
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Robust dual reconstruction systems and fusion frames; Springer; Acta Applicandae Mathematicae; 119; 1; 6-2012; 167-183
0167-8019
1572-9036
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100310
identifier_str_mv Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Robust dual reconstruction systems and fusion frames; Springer; Acta Applicandae Mathematicae; 119; 1; 6-2012; 167-183
0167-8019
1572-9036
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10440-011-9667-x
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1112.1654
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10440-011-9667-x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
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 13.087074

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