A numerical exploration of compressed sampling recovery

This paper explores numerically the efficiency of P 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 l(1) 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. (C) 2009 Elsevier Inc. All rights reserved.