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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/2662
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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 Técnicas2025-09-29T10:39:49Zoai: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:34982025-09-29 10:39:49.594CONICET 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 |
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CONICET Digital (CONICET) |
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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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