A Numerical Exploration of Compressed Sampling Recovery

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

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