Optimal non-linear models for sparsity and sampling

Given a set of vectors (the data) in a Hilbert space ℋ, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Aldroubi, A., Cabrelli, C., Molter, U.
Formato: JOUR
Materias:
Compressed sensing
Frames
Sampling
Sparsity
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10695869_v14_n5-6_p793_Aldroubi
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_10695869_v14_n5-6_p793_Aldroubi
record_format dspace
spelling todo:paper_10695869_v14_n5-6_p793_Aldroubi2023-10-03T16:02:13Z Optimal non-linear models for sparsity and sampling Aldroubi, A. Cabrelli, C. Molter, U. Compressed sensing Frames Sampling Sparsity Given a set of vectors (the data) in a Hilbert space ℋ, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in union of subspaces. The results are proved in a general setting and then applied to the case of low dimensional subspaces of ℋN and to infinite dimensional shift-invariant spaces in L 2(ℋd ). We also present an iterative search algorithm for finding the solution subspaces. These results are tightly connected to the new emergent theories of compressed sensing and dictionary design, signal models for signals with finite rate of innovation, and the subspace segmentation problem. © 2008 Birkhäuser Boston. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10695869_v14_n5-6_p793_Aldroubi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Compressed sensing
Frames
Sampling
Sparsity
spellingShingle Compressed sensing
Frames
Sampling
Sparsity
Aldroubi, A.
Cabrelli, C.
Molter, U.
Optimal non-linear models for sparsity and sampling
topic_facet Compressed sensing
Frames
Sampling
Sparsity
description Given a set of vectors (the data) in a Hilbert space ℋ, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in union of subspaces. The results are proved in a general setting and then applied to the case of low dimensional subspaces of ℋN and to infinite dimensional shift-invariant spaces in L 2(ℋd ). We also present an iterative search algorithm for finding the solution subspaces. These results are tightly connected to the new emergent theories of compressed sensing and dictionary design, signal models for signals with finite rate of innovation, and the subspace segmentation problem. © 2008 Birkhäuser Boston.
format JOUR
author Aldroubi, A.
Cabrelli, C.
Molter, U.
author_facet Aldroubi, A.
Cabrelli, C.
Molter, U.
author_sort Aldroubi, A.
title Optimal non-linear models for sparsity and sampling
title_short Optimal non-linear models for sparsity and sampling
title_full Optimal non-linear models for sparsity and sampling
title_fullStr Optimal non-linear models for sparsity and sampling
title_full_unstemmed Optimal non-linear models for sparsity and sampling
title_sort optimal non-linear models for sparsity and sampling
url http://hdl.handle.net/20.500.12110/paper_10695869_v14_n5-6_p793_Aldroubi
work_keys_str_mv AT aldroubia optimalnonlinearmodelsforsparsityandsampling
AT cabrellic optimalnonlinearmodelsforsparsityandsampling
AT molteru optimalnonlinearmodelsforsparsityandsampling
_version_ 1782027192959500288

Ejemplares similares