A numerical exploration of compressed sampling recovery
Fadili, Jalal; Peyré, Gabriel; Dossal, Charles (2010), A numerical exploration of compressed sampling recovery, Linear Algebra and its Applications, 432, 7, p. 1663-1679. http://dx.doi.org/10.1016/j.laa.2009.11.022
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00402455/en/
Journal nameLinear Algebra and its Applications
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Abstract (EN)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-conditioned. 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.
Subjects / KeywordsCompressed sensing; Restricted isometry constant; Polytopes; ℓ1 minimization
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