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 Annali dell'Universita di Ferrara (2012) ??--??
 Versions disponibles : v1 (31-01-2011) v2 (30-05-2011)
 Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions
 (2012)
 Efficient recovery of smooth functions which are $s$-sparse with respect to the base of so--called Prolate Spheroidal Wave Functions from a small number of random sampling points is considered. The main ingredient in the design of both the algorithms we propose here consists in establishing a uniform $L^\infty$ bound on the measurement ensembles which constitute the columns of the sensing matrix. Such a bound provides us with the Restricted Isometry Property for this rectangular random matrix, which leads to either the exact recovery property or the ''best $s$-term approximation" of the original signal by means of the $\ell^1$ minimization program. The first algorithm considers only a restricted number of columns for which the $L^\infty$ holds as a consequence of the fact that eigenvalues of the Bergman's restriction operator are close to 1 whereas the second one allows for a wider system of PSWF by taking advantage of a preconditioning technique. Numerical examples are spread throughout the text to illustrate the results.
 1 : Istituto per le Applicazioni del Calcolo "Mauro Picone" (IAC) Consiglio Nazionale delle Ricerche
 Domaine : Mathématiques/Analyse numériqueSciences de l'ingénieur/Traitement du signal et de l'imageInformatique/Traitement du signal et de l'image
 Mots Clés : Doubly orthogonal sequences – Slepian functions – Compressed sensing – Restricted isometry property – Preconditioning – Bandlimited extrapolation
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 hal-00560962, version 2 http://hal.archives-ouvertes.fr/hal-00560962 oai:hal.archives-ouvertes.fr:hal-00560962 Contributeur : Laurent Gosse <> Soumis le : Lundi 30 Mai 2011, 13:30:24 Dernière modification le : Jeudi 3 Mai 2012, 11:41:47