Title :

Sparsity-Based Estimation Bounds With Corrupted Measurements

Author(s) :

Boyer, Remy [Auteur]
Laboratoire des signaux et systèmes [L2S]
Larzabal, Pascal [Auteur]
Systèmes et Applications des Technologies de l'Information et de l'Energie [SATIE]

Journal title :

Signal Processing

Pages :

86-93

Publisher :

Elsevier

Publication date :

2018-02-01

ISSN :

0165-1684

English keyword(s) :

Compressed sensing
corrupted measurements
Cramér-Rao

HAL domain(s) :

Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]
Statistiques [stat]/Applications [stat.AP]

English abstract : [en]

In typical Compressed Sensing operational contexts, the measurement vector y is often partially corrupted. The estimation of a sparse vector acting on the entire support set exhibits very poor estimation performance. It ...
Show more >In typical Compressed Sensing operational contexts, the measurement vector y is often partially corrupted. The estimation of a sparse vector acting on the entire support set exhibits very poor estimation performance. It is crucial to estimate set I uc containing the indexes of the uncorrupted measures. As I uc and its cardinality |I uc | < N are unknown, each sample of vector y follows an i.i.d. Bernoulli prior of probability P uc , leading to a Binomial-distributed car-dinality. In this context, we derive and analyze the performance lower bound on the Bayesian Mean Square Error (BMSE) on a |S|-sparse vector where each random entry is the product of a continuous variable and a Bernoulli variable of probability P and |S| |Iuc| follows a hierarchical Binomial distribution on set {1,. .. , |I uc | − 1}. The derived lower bounds do not belong to the family of " oracle " or " genie-aided " bounds since our a priori knowledge on support I uc and its cardinality is limited to probability P uc. In this context, very compact and simple expressions of the Expected Cramer-Rao Bound (ECRB) are proposed. Finally, the proposed lower bounds are compared to standard estimation strategies robust to an impulsive (sparse) noise.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Méthodes d'apprentissage pour les très grands réseaux d'antennes en radioastronomie

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL