A numerical exploration of compressed sampling recovery

作者：Dossal Charles^*; Peyre Gabriel; Fadili Jalal

来源：Linear Algebra and Its Applications, 2010, 432(7): 1663-1679.

DOI：10.1016/j.laa.2009.11.022

• Compressed sensing
• l(1) minimization
• Restricted isometry constant
• Polytopes

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.

• 出版日期2010-3-15