Aliasing and oblique dual pair designs for consistent sampling

Autores
Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study some aspects of oblique duality between finite sequences of vectors FF and GG lying in finite dimensional subspaces WW and VV, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to FF lying in VV. We compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for FF with norm restrictions; as an application, we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible, among oblique duals with norm restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces VV and WW has in oblique duality. We apply this analysis to compute those rigid rotations U for WW such that the canonical oblique dual of U⋅FU⋅F minimize every convex potential; we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations U for WW such that the canonical oblique dual pair associated to U⋅FU⋅F minimize the aliasing. We point out that these two last problems are intrinsic to oblique duality, within the context of consistent sampling.
Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Materia
marcos
mayorización
dualidad oblicua
Lidskii
frames
oblique duality
majorization
convex potentials
Lindii's theorem
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:11336/2662
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/2662
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Aliasing and oblique dual pair designs for consistent samplingBenac, Maria JoseMassey, Pedro GustavoStojanoff, Demetriomarcosmayorizacióndualidad oblicuaLidskiiframesoblique dualitymajorizationconvex potentialsLindii's theoremhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study some aspects of oblique duality between finite sequences of vectors FF and GG lying in finite dimensional subspaces WW and VV, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to FF lying in VV. We compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for FF with norm restrictions; as an application, we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible, among oblique duals with norm restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces VV and WW has in oblique duality. We apply this analysis to compute those rigid rotations U for WW such that the canonical oblique dual of U⋅FU⋅F minimize every convex potential; we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations U for WW such that the canonical oblique dual pair associated to U⋅FU⋅F minimize the aliasing. We point out that these two last problems are intrinsic to oblique duality, within the context of consistent sampling.Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaFil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaElsevier Science Inc2015-12-15info: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/11336/2662Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Aliasing and oblique dual pair designs for consistent sampling; Elsevier Science Inc; Linear Algebra And Its Applications; 487; 15-12-2015; 112-1450024-3795enginfo:eu-repo/semantics/altIdentifier/url/http://goo.gl/NSochQinfo:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/url/http://dx.doi/10.1016/j.laa.2015.09.007info:eu-repo/semantics/altIdentifier/ark/http://arxiv.org/pdf/1410.2809v1.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:12:10Zoai:ri.conicet.gov.ar:11336/2662instacron: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:34982025-10-22 12:12:10.291CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Aliasing and oblique dual pair designs for consistent sampling
title Aliasing and oblique dual pair designs for consistent sampling
spellingShingle Aliasing and oblique dual pair designs for consistent sampling
Benac, Maria Jose
marcos
mayorización
dualidad oblicua
Lidskii
frames
oblique duality
majorization
convex potentials
Lindii's theorem
title_short Aliasing and oblique dual pair designs for consistent sampling
title_full Aliasing and oblique dual pair designs for consistent sampling
title_fullStr Aliasing and oblique dual pair designs for consistent sampling
title_full_unstemmed Aliasing and oblique dual pair designs for consistent sampling
title_sort Aliasing and oblique dual pair designs for consistent sampling
dc.creator.none.fl_str_mv Benac, Maria Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author Benac, Maria Jose
author_facet Benac, Maria Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv marcos
mayorización
dualidad oblicua
Lidskii
frames
oblique duality
majorization
convex potentials
Lindii's theorem
topic marcos
mayorización
dualidad oblicua
Lidskii
frames
oblique duality
majorization
convex potentials
Lindii's theorem
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 study some aspects of oblique duality between finite sequences of vectors FF and GG lying in finite dimensional subspaces WW and VV, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to FF lying in VV. We compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for FF with norm restrictions; as an application, we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible, among oblique duals with norm restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces VV and WW has in oblique duality. We apply this analysis to compute those rigid rotations U for WW such that the canonical oblique dual of U⋅FU⋅F minimize every convex potential; we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations U for WW such that the canonical oblique dual pair associated to U⋅FU⋅F minimize the aliasing. We point out that these two last problems are intrinsic to oblique duality, within the context of consistent sampling.
Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
description In this paper we study some aspects of oblique duality between finite sequences of vectors FF and GG lying in finite dimensional subspaces WW and VV, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to FF lying in VV. We compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for FF with norm restrictions; as an application, we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible, among oblique duals with norm restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces VV and WW has in oblique duality. We apply this analysis to compute those rigid rotations U for WW such that the canonical oblique dual of U⋅FU⋅F minimize every convex potential; we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations U for WW such that the canonical oblique dual pair associated to U⋅FU⋅F minimize the aliasing. We point out that these two last problems are intrinsic to oblique duality, within the context of consistent sampling.
publishDate 2015
dc.date.none.fl_str_mv 2015-12-15
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/11336/2662
Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Aliasing and oblique dual pair designs for consistent sampling; Elsevier Science Inc; Linear Algebra And Its Applications; 487; 15-12-2015; 112-145
0024-3795
url http://hdl.handle.net/11336/2662
identifier_str_mv Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Aliasing and oblique dual pair designs for consistent sampling; Elsevier Science Inc; Linear Algebra And Its Applications; 487; 15-12-2015; 112-145
0024-3795
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://goo.gl/NSochQ
info:eu-repo/semantics/altIdentifier/doi/
info:eu-repo/semantics/altIdentifier/url/http://dx.doi/10.1016/j.laa.2015.09.007
info:eu-repo/semantics/altIdentifier/ark/http://arxiv.org/pdf/1410.2809v1.pdf
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
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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 12.982451

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