Stereographic wavelet frames on the sphere

Autores
Bogdanova, I.; Vandergheynst, P.; Antoine, J. P.; Jacques, L.; Morvidone, Marcela Alejandra
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we exploit the continuous wavelet transform (CWT) on the two-dimensional sphere S2, introduced previously by two of us, to build associated discrete wavelet frames. We first explore half-continuous frames, i.e., frames where the position remains a continuous variable, and then move on to a fully discrete theory. We introduce the notion of controlled frames, which reflects the particular nature of the underlying theory, in particular the apparent conflict between dilation and the compactness of the S2 manifold. We also highlight some implementation issues and provide numerical illustrations.
Fil: Bogdanova, I.. Swiss Federal Institute Of Technology Epfl, Lausanne;
Fil: Vandergheynst, P.. Swiss Federal Institute Of Technology Epfl, Lausanne;
Fil: Antoine, J. P.. Université Catholique de Louvain; Bélgica
Fil: Jacques, L.. Université Catholique de Louvain; Bélgica
Fil: Morvidone, Marcela Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
CONTINUOUS WAVELET TRANSFORM
CONTROLLED FRAMES
DISCRETE WAVELET FRAMES
HALF-CONTINUOUS FRAMES
SPHERICAL 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:11336/100628
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/100628
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Stereographic wavelet frames on the sphereBogdanova, I.Vandergheynst, P.Antoine, J. P.Jacques, L.Morvidone, Marcela AlejandraCONTINUOUS WAVELET TRANSFORMCONTROLLED FRAMESDISCRETE WAVELET FRAMESHALF-CONTINUOUS FRAMESSPHERICAL WAVELETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we exploit the continuous wavelet transform (CWT) on the two-dimensional sphere S2, introduced previously by two of us, to build associated discrete wavelet frames. We first explore half-continuous frames, i.e., frames where the position remains a continuous variable, and then move on to a fully discrete theory. We introduce the notion of controlled frames, which reflects the particular nature of the underlying theory, in particular the apparent conflict between dilation and the compactness of the S2 manifold. We also highlight some implementation issues and provide numerical illustrations.Fil: Bogdanova, I.. Swiss Federal Institute Of Technology Epfl, Lausanne; Fil: Vandergheynst, P.. Swiss Federal Institute Of Technology Epfl, Lausanne; Fil: Antoine, J. P.. Université Catholique de Louvain; BélgicaFil: Jacques, L.. Université Catholique de Louvain; BélgicaFil: Morvidone, Marcela Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaAcademic Press Inc Elsevier Science2005-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/100628Bogdanova, I.; Vandergheynst, P.; Antoine, J. P.; Jacques, L.; Morvidone, Marcela Alejandra; Stereographic wavelet frames on the sphere; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 19; 2; 9-2005; 223-2521063-5203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.acha.2005.05.001info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:41:48Zoai:ri.conicet.gov.ar:11336/100628instacron: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 09:41:49.106CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stereographic wavelet frames on the sphere
title Stereographic wavelet frames on the sphere
spellingShingle Stereographic wavelet frames on the sphere
Bogdanova, I.
CONTINUOUS WAVELET TRANSFORM
CONTROLLED FRAMES
DISCRETE WAVELET FRAMES
HALF-CONTINUOUS FRAMES
SPHERICAL WAVELETS
title_short Stereographic wavelet frames on the sphere
title_full Stereographic wavelet frames on the sphere
title_fullStr Stereographic wavelet frames on the sphere
title_full_unstemmed Stereographic wavelet frames on the sphere
title_sort Stereographic wavelet frames on the sphere
dc.creator.none.fl_str_mv Bogdanova, I.
Vandergheynst, P.
Antoine, J. P.
Jacques, L.
Morvidone, Marcela Alejandra
author Bogdanova, I.
author_facet Bogdanova, I.
Vandergheynst, P.
Antoine, J. P.
Jacques, L.
Morvidone, Marcela Alejandra
author_role author
author2 Vandergheynst, P.
Antoine, J. P.
Jacques, L.
Morvidone, Marcela Alejandra
author2_role author
author
author
author
dc.subject.none.fl_str_mv CONTINUOUS WAVELET TRANSFORM
CONTROLLED FRAMES
DISCRETE WAVELET FRAMES
HALF-CONTINUOUS FRAMES
SPHERICAL WAVELETS
topic CONTINUOUS WAVELET TRANSFORM
CONTROLLED FRAMES
DISCRETE WAVELET FRAMES
HALF-CONTINUOUS FRAMES
SPHERICAL 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 paper we exploit the continuous wavelet transform (CWT) on the two-dimensional sphere S2, introduced previously by two of us, to build associated discrete wavelet frames. We first explore half-continuous frames, i.e., frames where the position remains a continuous variable, and then move on to a fully discrete theory. We introduce the notion of controlled frames, which reflects the particular nature of the underlying theory, in particular the apparent conflict between dilation and the compactness of the S2 manifold. We also highlight some implementation issues and provide numerical illustrations.
Fil: Bogdanova, I.. Swiss Federal Institute Of Technology Epfl, Lausanne;
Fil: Vandergheynst, P.. Swiss Federal Institute Of Technology Epfl, Lausanne;
Fil: Antoine, J. P.. Université Catholique de Louvain; Bélgica
Fil: Jacques, L.. Université Catholique de Louvain; Bélgica
Fil: Morvidone, Marcela Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description In this paper we exploit the continuous wavelet transform (CWT) on the two-dimensional sphere S2, introduced previously by two of us, to build associated discrete wavelet frames. We first explore half-continuous frames, i.e., frames where the position remains a continuous variable, and then move on to a fully discrete theory. We introduce the notion of controlled frames, which reflects the particular nature of the underlying theory, in particular the apparent conflict between dilation and the compactness of the S2 manifold. We also highlight some implementation issues and provide numerical illustrations.
publishDate 2005
dc.date.none.fl_str_mv 2005-09
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/11336/100628
Bogdanova, I.; Vandergheynst, P.; Antoine, J. P.; Jacques, L.; Morvidone, Marcela Alejandra; Stereographic wavelet frames on the sphere; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 19; 2; 9-2005; 223-252
1063-5203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100628
identifier_str_mv Bogdanova, I.; Vandergheynst, P.; Antoine, J. P.; Jacques, L.; Morvidone, Marcela Alejandra; Stereographic wavelet frames on the sphere; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 19; 2; 9-2005; 223-252
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.2005.05.001
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
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
_version_ 1844613318489145344
score 13.070432

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