Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)

Autores
Aldroubi, Akram; Cabrelli, Carlos; Molter, Ursula Maria
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, we develop a general method for constructing wavelets {| det Aj|1/2ψ(Ajx-xj,k): j ∈ J, k ∈ K} on irregular lattices of the form X = {xj,k ∈ ℝd: j ∈ J, k ∈ K}, and with an arbitrary countable family of invertible d × d matrices {Aj ∈ GL d(ℝ): j ∈ J} that do not necessarily have a group structure. This wavelet construction is a particular case of general atomic frame decompositions of L2(ℝd) developed in this article, that allow other time frequency decompositions such as nonharmonic Gabor frames with nonuniform covering of the Euclidean space ℝ d. Possible applications include image and video compression, speech coding, image and digital data transmission, image analysis, estimations and detection, and seismology.
Fil: Aldroubi, Akram. Vanderbilt University; Estados Unidos
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
FRAMES
IRREGULAR SAMPLING
WAVELET SETS
WAVELETS
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:11336/151186
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/151186
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)Aldroubi, AkramCabrelli, CarlosMolter, Ursula MariaFRAMESIRREGULAR SAMPLINGWAVELET SETSWAVELETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article, we develop a general method for constructing wavelets {| det Aj|1/2ψ(Ajx-xj,k): j ∈ J, k ∈ K} on irregular lattices of the form X = {xj,k ∈ ℝd: j ∈ J, k ∈ K}, and with an arbitrary countable family of invertible d × d matrices {Aj ∈ GL d(ℝ): j ∈ J} that do not necessarily have a group structure. This wavelet construction is a particular case of general atomic frame decompositions of L2(ℝd) developed in this article, that allow other time frequency decompositions such as nonharmonic Gabor frames with nonuniform covering of the Euclidean space ℝ d. Possible applications include image and video compression, speech coding, image and digital data transmission, image analysis, estimations and detection, and seismology.Fil: Aldroubi, Akram. Vanderbilt University; Estados UnidosFil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc Elsevier Science2004-12info: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/11336/151186Aldroubi, Akram; Cabrelli, Carlos; Molter, Ursula Maria; Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd); Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 17; 12-2004; 119-1401063-5203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.acha.2004.03.005info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1063520304000442?via%3Dihubinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0703438info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:46:33Zoai:ri.conicet.gov.ar:11336/151186instacron: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 10:46:33.524CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
title Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
spellingShingle Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
Aldroubi, Akram
FRAMES
IRREGULAR SAMPLING
WAVELET SETS
WAVELETS
title_short Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
title_full Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
title_fullStr Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
title_full_unstemmed Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
title_sort Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd)
dc.creator.none.fl_str_mv Aldroubi, Akram
Cabrelli, Carlos
Molter, Ursula Maria
author Aldroubi, Akram
author_facet Aldroubi, Akram
Cabrelli, Carlos
Molter, Ursula Maria
author_role author
author2 Cabrelli, Carlos
Molter, Ursula Maria
author2_role author
author
dc.subject.none.fl_str_mv FRAMES
IRREGULAR SAMPLING
WAVELET SETS
WAVELETS
topic FRAMES
IRREGULAR SAMPLING
WAVELET SETS
WAVELETS
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 develop a general method for constructing wavelets {| det Aj|1/2ψ(Ajx-xj,k): j ∈ J, k ∈ K} on irregular lattices of the form X = {xj,k ∈ ℝd: j ∈ J, k ∈ K}, and with an arbitrary countable family of invertible d × d matrices {Aj ∈ GL d(ℝ): j ∈ J} that do not necessarily have a group structure. This wavelet construction is a particular case of general atomic frame decompositions of L2(ℝd) developed in this article, that allow other time frequency decompositions such as nonharmonic Gabor frames with nonuniform covering of the Euclidean space ℝ d. Possible applications include image and video compression, speech coding, image and digital data transmission, image analysis, estimations and detection, and seismology.
Fil: Aldroubi, Akram. Vanderbilt University; Estados Unidos
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this article, we develop a general method for constructing wavelets {| det Aj|1/2ψ(Ajx-xj,k): j ∈ J, k ∈ K} on irregular lattices of the form X = {xj,k ∈ ℝd: j ∈ J, k ∈ K}, and with an arbitrary countable family of invertible d × d matrices {Aj ∈ GL d(ℝ): j ∈ J} that do not necessarily have a group structure. This wavelet construction is a particular case of general atomic frame decompositions of L2(ℝd) developed in this article, that allow other time frequency decompositions such as nonharmonic Gabor frames with nonuniform covering of the Euclidean space ℝ d. Possible applications include image and video compression, speech coding, image and digital data transmission, image analysis, estimations and detection, and seismology.
publishDate 2004
dc.date.none.fl_str_mv 2004-12
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/11336/151186
Aldroubi, Akram; Cabrelli, Carlos; Molter, Ursula Maria; Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd); Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 17; 12-2004; 119-140
1063-5203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/151186
identifier_str_mv Aldroubi, Akram; Cabrelli, Carlos; Molter, Ursula Maria; Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(ℝd); Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 17; 12-2004; 119-140
1063-5203
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.acha.2004.03.005
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1063520304000442?via%3Dihub
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0703438
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 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 13.070432

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