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Journal Articles Linear Algebra and its Applications Year : 2010

A Numerical Exploration of Compressed Sampling Recovery

Charles H Dossal
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Jalal M. Fadili


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.
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Dates and versions

hal-00402455 , version 1 (07-07-2009)
hal-00402455 , version 2 (27-11-2009)



Charles H Dossal, Gabriel Peyré, Jalal M. Fadili. A Numerical Exploration of Compressed Sampling Recovery. Linear Algebra and its Applications, 2010, 432 (7), pp.1663-1679. ⟨10.1016/j.laa.2009.11.022⟩. ⟨hal-00402455v2⟩
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