A Numerical Exploration of Compressed Sampling Recovery

Fadili, Jalal; Peyré, Gabriel; Dossal, Charles

Fadili, Jalal; Peyré, Gabriel; Dossal, Charles (2009-04), A Numerical Exploration of Compressed Sampling Recovery, SPARS'09, Signal Processing with Adaptive Sparse Structured Representations, 2009-04, Saint-Malo, France

Type

Communication / Conférence

External document link

http://hal.archives-ouvertes.fr/hal-00365028/en/

Date

2009-04

Conference title

SPARS'09, Signal Processing with Adaptive Sparse Structured Representations

Conference date

2009-04

Conference city

Saint-Malo

Conference country

France

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Author(s)

Fadili, Jalal
Peyré, Gabriel
Dossal, Charles

Abstract (EN)

This paper explores numerically the efficiency of $\lun$ minimization for the recovery of sparse signals from compressed sampling measurements in the noiseless case. Inspired by topological criteria for $\lun$-identifiability, a greedy algorithm computes sparse vectors that are difficult to recover by $\ell_1$-minimization. We evaluate numerically the theoretical analysis without resorting to Monte-Carlo sampling, which tends to avoid worst case scenarios. This allows one to challenge sparse recovery conditions based on polytope projection and on the restricted isometry property.

Subjects / Keywords

L1 minimization; sparsity; Compressed sensing