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Aldroubi, A.; Cabrelli, C.; Molter, U. "Optimal non-linear models for sparsity and sampling" (2008) Journal of Fourier Analysis and Applications. 14(5-6):793-812
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Abstract:

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.

Registro:

Documento: Artículo
Título:Optimal non-linear models for sparsity and sampling
Autor:Aldroubi, A.; Cabrelli, C.; Molter, U.
Filiación:Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, United States
Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Capital Federal, Buenos Aires, Argentina
Conicet, Buenos Aires, Argentina
Palabras clave:Compressed sensing; Frames; Sampling; Sparsity
Año:2008
Volumen:14
Número:5-6
Página de inicio:793
Página de fin:812
DOI: http://dx.doi.org/10.1007/s00041-008-9040-2
Título revista:Journal of Fourier Analysis and Applications
Título revista abreviado:J. Fourier Anal. Appl.
ISSN:10695869
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v14_n5-6_p793_Aldroubi

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Citas:

---------- APA ----------
Aldroubi, A., Cabrelli, C. & Molter, U. (2008) . Optimal non-linear models for sparsity and sampling. Journal of Fourier Analysis and Applications, 14(5-6), 793-812.
http://dx.doi.org/10.1007/s00041-008-9040-2
---------- CHICAGO ----------
Aldroubi, A., Cabrelli, C., Molter, U. "Optimal non-linear models for sparsity and sampling" . Journal of Fourier Analysis and Applications 14, no. 5-6 (2008) : 793-812.
http://dx.doi.org/10.1007/s00041-008-9040-2
---------- MLA ----------
Aldroubi, A., Cabrelli, C., Molter, U. "Optimal non-linear models for sparsity and sampling" . Journal of Fourier Analysis and Applications, vol. 14, no. 5-6, 2008, pp. 793-812.
http://dx.doi.org/10.1007/s00041-008-9040-2
---------- VANCOUVER ----------
Aldroubi, A., Cabrelli, C., Molter, U. Optimal non-linear models for sparsity and sampling. J. Fourier Anal. Appl. 2008;14(5-6):793-812.
http://dx.doi.org/10.1007/s00041-008-9040-2