 |
|
|
|
| HAL : hal-00560962, version 2 |
| DOI : 10.1007/s11565-012-0159-3 |
| Fiche détaillée |  Récupérer au format |
|
|
| 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 |
|
|
| Laurent Gosse 1 |
|
|
| (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 numérique Sciences de l'ingénieur/Traitement du signal et de l'image Informatique/Traitement du signal et de l'image |
|
|
| Doubly orthogonal sequences – Slepian functions – Compressed sensing – Restricted isometry property – Preconditioning – Bandlimited extrapolation |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| 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 | |
