Sampling in a union of frame generated subspaces

A new paradigm in sampling theory has been developed recently by Lu and Do. In this new approach the classical linear model is replaced by a non-linear, but structured, model consisting of a union of subspaces. This is the natural approach for the new theory of compressed sampling, representation of...

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Detalles Bibliográficos
Autores principales:	Anastasio, Magalí, Cabrelli, Carlos Alberto
Publicado:	2009
Materias:	Angle between subspaces Compressed sampling Frames Gramian operator Riesz basis Sampling Shift-invariant spaces
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v8_n3_p261_Anastasio http://hdl.handle.net/20.500.12110/paper_15306429_v8_n3_p261_Anastasio
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15306429_v8_n3_p261_Anastasio
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spelling	paper:paper_15306429_v8_n3_p261_Anastasio2023-06-08T16:19:45Z Sampling in a union of frame generated subspaces Anastasio, Magalí Cabrelli, Carlos Alberto Angle between subspaces Compressed sampling Frames Gramian operator Riesz basis Sampling Shift-invariant spaces A new paradigm in sampling theory has been developed recently by Lu and Do. In this new approach the classical linear model is replaced by a non-linear, but structured, model consisting of a union of subspaces. This is the natural approach for the new theory of compressed sampling, representation of sparse signals, and signals with finite rate of innovation. In this article we extend the theory of Lu and Do, for the case that the subspaces in the union are shift-invariant spaces. We describe the subspaces by means of frame generators instead of orthonormal bases. We show that the one-to-one and stability conditions for the sampling operator are valid for this more general case. © 2009 SAMPLING PUBLISHING. Fil:Anastasio, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v8_n3_p261_Anastasio http://hdl.handle.net/20.500.12110/paper_15306429_v8_n3_p261_Anastasio
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Angle between subspaces Compressed sampling Frames Gramian operator Riesz basis Sampling Shift-invariant spaces
spellingShingle	Angle between subspaces Compressed sampling Frames Gramian operator Riesz basis Sampling Shift-invariant spaces Anastasio, Magalí Cabrelli, Carlos Alberto Sampling in a union of frame generated subspaces
topic_facet	Angle between subspaces Compressed sampling Frames Gramian operator Riesz basis Sampling Shift-invariant spaces
description	A new paradigm in sampling theory has been developed recently by Lu and Do. In this new approach the classical linear model is replaced by a non-linear, but structured, model consisting of a union of subspaces. This is the natural approach for the new theory of compressed sampling, representation of sparse signals, and signals with finite rate of innovation. In this article we extend the theory of Lu and Do, for the case that the subspaces in the union are shift-invariant spaces. We describe the subspaces by means of frame generators instead of orthonormal bases. We show that the one-to-one and stability conditions for the sampling operator are valid for this more general case. © 2009 SAMPLING PUBLISHING.
author	Anastasio, Magalí Cabrelli, Carlos Alberto
author_facet	Anastasio, Magalí Cabrelli, Carlos Alberto
author_sort	Anastasio, Magalí
title	Sampling in a union of frame generated subspaces
title_short	Sampling in a union of frame generated subspaces
title_full	Sampling in a union of frame generated subspaces
title_fullStr	Sampling in a union of frame generated subspaces
title_full_unstemmed	Sampling in a union of frame generated subspaces
title_sort	sampling in a union of frame generated subspaces
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v8_n3_p261_Anastasio http://hdl.handle.net/20.500.12110/paper_15306429_v8_n3_p261_Anastasio
work_keys_str_mv	AT anastasiomagali samplinginaunionofframegeneratedsubspaces AT cabrellicarlosalberto samplinginaunionofframegeneratedsubspaces
_version_	1768546460362604544

Sampling in a union of frame generated subspaces

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