A Numerical Exploration of Compressed Sampling Recovery

Charles H Dossal (1) , Gabriel Peyré (2) , Jalal M. Fadili (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Equipe Image - Laboratoire GREYC - UMR6072

This paper explores numerically the efficiency of L1 minimization for the recovery of sparse signals from compressed sampling measurements in the noiseless case. This numerical exploration is driven by a new greedy pursuit algorithm that computes sparse vectors that are difficult to recover by L1 minimization. The supports of these pathological vectors are also used to select sub-matrices that are ill-conditionned. This allows us to challenge theoretical identifiability criteria based on polytopes analysis and on restricted isometry conditions. We evaluate numerically the theoretical analysis without resorting to Monte-Carlo sampling, which tends to avoid worst case scenarios.

Mots clés: polytopes; Compressed sensing; L1 minimization; restricted isometry constant; polytopes.

Domaines: Analyse numérique [math.NA]

Charles H Dossal, Gabriel Peyré, Jalal M. Fadili. A Numerical Exploration of Compressed Sampling Recovery. Linear Algebra and its Applications, 2009. ⟨hal-00402455v1⟩