Laboratoire de Physique Théorique et Modèles Statistiques

Séminaire du LPTMS : Yoshiyuki Kabashima

A statistical mechanical approach to compressed sensing

Yoshiyuki Kabashima, Tokyo Institute of Technology, Japan

We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated from its linear transformation under the assumption that the number of non-zero elements of x is typically limited to \rho N (0 \le \rho \le 1). Problems of this kind are very relevant for various modern sensing (sampling, imaging, etc.) techniques such as radar measurement, computed tomography and so on. In efforts toward designing efficient reconstruction schemes exploiting the prior knowledge of sparsity, minimization of a cost function with respect to the so-called Lp-norm of x under the P constraints has been actively studied these days [1].In this talk, we introduce our recent attempt [2], which is based on the replica method of statistical mechanics, for evaluating a critical relation between \alpha = P/N and \rho for successfully reconstructing the original vector x by the minimization.

References:
[1] http://en.wikipedia.org/wiki/Compressed_sensing
[2] YK, T. Wadayama and T. Tanaka, J. Stat. Mech. (2009) L09003 (12 pages)

Vendredi 4 juin à 11h

LPTMS-batiment 100, salle 201, Orsay


Calendrier des séminaires

Mai
Juillet
Juin 2010
lun. mar. mer. jeu. ven.
 
1
16:00» Seminaire LPTMS: Uzy Smilansky (Weizmann)
2
3
14:00» Séminaire commun LPT-LPTMS : Petr Sulc
4
11:00» Séminaire du LPTMS : Yoshiyuki Kabashima
7
14:00» Séminaire PHYSTAT-SUD : Jon Keating
8
11:00» Seminaire LPTMS : Luigi Cantini (LPT ENS)
9
10
11
14
15
11:00» Seminaire LPTMS: Rhoda Hawkins
16
17
18
14:00» Séminaire Physique Biologique et Systèmes Complexes : Guillaume Romet-Lemonne
21
22
11:00» Semianire LPTMS: Martin Lenz (Chicago)
23
24
16:00» Séminaire du LPTMS : Gunnar Boldhaus
25
10:30» Soutenance de thèse : Carlos Eduardo Alvarez Cabrera
15:00» Séminaire exceptionnel du LPTMS : Paolo Solinas
28
29
11:00» Seminaire LPTMS: Celine Nadal, Alvaro Rojo
30