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, M., Cabrelli, C.
Formato: JOUR
Materias:
Angle between subspaces
Compressed sampling
Frames
Gramian operator
Riesz basis
Sampling
Shift-invariant spaces
Acceso en línea: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 todo:paper_15306429_v8_n3_p261_Anastasio
record_format dspace
spelling todo:paper_15306429_v8_n3_p261_Anastasio2023-10-03T16:21:16Z Sampling in a union of frame generated subspaces Anastasio, M. Cabrelli, C. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, M.
Cabrelli, C.
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.
format JOUR
author Anastasio, M.
Cabrelli, C.
author_facet Anastasio, M.
Cabrelli, C.
author_sort Anastasio, M.
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
url http://hdl.handle.net/20.500.12110/paper_15306429_v8_n3_p261_Anastasio
work_keys_str_mv AT anastasiom samplinginaunionofframegeneratedsubspaces
AT cabrellic samplinginaunionofframegeneratedsubspaces
_version_ 1807322776469504000

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