Random periodic sampling patterns for shift-invariant spaces

Autores
Antezana, Jorge Abel; Carbajal, Diana Agustina; Romero, Jose Luis Fernando
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the number of frequency profiles by a logarithmic factor. The signal model includes bandlimited functions with multi-band spectra. While in this wellstudied setting delicate constructions provide sampling strategies that meet the information theoretic benchmark of Shannon and Landau, the sampling pattern that we consider provides, at the price of a logarithmic oversampling factor, a simple alternative that is accompanied by favorable a priori stability margins (snug frames). More generally, we also treat bandlimited functions with arbitrary compact spectra, and different measures of their complexity and approximation rates by integer tiles. At the technical level, we elaborate on recent work on relevant sampling, with the key difference that the reconstruction guarantees that we provide hold uniformly for all signals, rather than for a subset of well-concentrated ones. This is achieved by methods of concentration of measure formulated on the Zak domain.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Carbajal, Diana Agustina. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Romero, Jose Luis Fernando. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
MULTITILE SPECTRA
SHIFT INVARIANT SPACES
ZAK TRANSFORM
RANDOM SAMPLING
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:11336/241722
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Random periodic sampling patterns for shift-invariant spacesAntezana, Jorge AbelCarbajal, Diana AgustinaRomero, Jose Luis FernandoMULTITILE SPECTRASHIFT INVARIANT SPACESZAK TRANSFORMRANDOM SAMPLINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the number of frequency profiles by a logarithmic factor. The signal model includes bandlimited functions with multi-band spectra. While in this wellstudied setting delicate constructions provide sampling strategies that meet the information theoretic benchmark of Shannon and Landau, the sampling pattern that we consider provides, at the price of a logarithmic oversampling factor, a simple alternative that is accompanied by favorable a priori stability margins (snug frames). More generally, we also treat bandlimited functions with arbitrary compact spectra, and different measures of their complexity and approximation rates by integer tiles. At the technical level, we elaborate on recent work on relevant sampling, with the key difference that the reconstruction guarantees that we provide hold uniformly for all signals, rather than for a subset of well-concentrated ones. This is achieved by methods of concentration of measure formulated on the Zak domain.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Carbajal, Diana Agustina. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Romero, Jose Luis Fernando. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaInstitute of Electrical and Electronics Engineers2024-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/241722Antezana, Jorge Abel; Carbajal, Diana Agustina; Romero, Jose Luis Fernando; Random periodic sampling patterns for shift-invariant spaces; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 70; 6; 6-2024; 3855-38630018-94481557-9654CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/10266375info:eu-repo/semantics/altIdentifier/doi/10.1109/TIT.2023.3320289info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2305.15261info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:19:44Zoai:ri.conicet.gov.ar:11336/241722instacron: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:34982025-09-29 10:19:45.096CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Random periodic sampling patterns for shift-invariant spaces
title Random periodic sampling patterns for shift-invariant spaces
spellingShingle Random periodic sampling patterns for shift-invariant spaces
Antezana, Jorge Abel
MULTITILE SPECTRA
SHIFT INVARIANT SPACES
ZAK TRANSFORM
RANDOM SAMPLING
title_short Random periodic sampling patterns for shift-invariant spaces
title_full Random periodic sampling patterns for shift-invariant spaces
title_fullStr Random periodic sampling patterns for shift-invariant spaces
title_full_unstemmed Random periodic sampling patterns for shift-invariant spaces
title_sort Random periodic sampling patterns for shift-invariant spaces
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Carbajal, Diana Agustina
Romero, Jose Luis Fernando
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Carbajal, Diana Agustina
Romero, Jose Luis Fernando
author_role author
author2 Carbajal, Diana Agustina
Romero, Jose Luis Fernando
author2_role author
author
dc.subject.none.fl_str_mv MULTITILE SPECTRA
SHIFT INVARIANT SPACES
ZAK TRANSFORM
RANDOM SAMPLING
topic MULTITILE SPECTRA
SHIFT INVARIANT SPACES
ZAK TRANSFORM
RANDOM SAMPLING
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 consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the number of frequency profiles by a logarithmic factor. The signal model includes bandlimited functions with multi-band spectra. While in this wellstudied setting delicate constructions provide sampling strategies that meet the information theoretic benchmark of Shannon and Landau, the sampling pattern that we consider provides, at the price of a logarithmic oversampling factor, a simple alternative that is accompanied by favorable a priori stability margins (snug frames). More generally, we also treat bandlimited functions with arbitrary compact spectra, and different measures of their complexity and approximation rates by integer tiles. At the technical level, we elaborate on recent work on relevant sampling, with the key difference that the reconstruction guarantees that we provide hold uniformly for all signals, rather than for a subset of well-concentrated ones. This is achieved by methods of concentration of measure formulated on the Zak domain.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Carbajal, Diana Agustina. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Romero, Jose Luis Fernando. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the number of frequency profiles by a logarithmic factor. The signal model includes bandlimited functions with multi-band spectra. While in this wellstudied setting delicate constructions provide sampling strategies that meet the information theoretic benchmark of Shannon and Landau, the sampling pattern that we consider provides, at the price of a logarithmic oversampling factor, a simple alternative that is accompanied by favorable a priori stability margins (snug frames). More generally, we also treat bandlimited functions with arbitrary compact spectra, and different measures of their complexity and approximation rates by integer tiles. At the technical level, we elaborate on recent work on relevant sampling, with the key difference that the reconstruction guarantees that we provide hold uniformly for all signals, rather than for a subset of well-concentrated ones. This is achieved by methods of concentration of measure formulated on the Zak domain.
publishDate 2024
dc.date.none.fl_str_mv 2024-06
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/11336/241722
Antezana, Jorge Abel; Carbajal, Diana Agustina; Romero, Jose Luis Fernando; Random periodic sampling patterns for shift-invariant spaces; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 70; 6; 6-2024; 3855-3863
0018-9448
1557-9654
CONICET Digital
CONICET
url http://hdl.handle.net/11336/241722
identifier_str_mv Antezana, Jorge Abel; Carbajal, Diana Agustina; Romero, Jose Luis Fernando; Random periodic sampling patterns for shift-invariant spaces; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 70; 6; 6-2024; 3855-3863
0018-9448
1557-9654
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/10266375
info:eu-repo/semantics/altIdentifier/doi/10.1109/TIT.2023.3320289
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2305.15261
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
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
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 13.070432

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