A Numerical Exploration of Compressed Sampling Recovery
Fadili, Jalal; Peyré, Gabriel; Dossal, Charles (2009-04), A Numerical Exploration of Compressed Sampling Recovery, SPARS'09, Signal Processing with Adaptive Sparse Structured Representations, 2009-04, Saint-Malo, France
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00365028/en/
Conference titleSPARS'09, Signal Processing with Adaptive Sparse Structured Representations
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Abstract (EN)This paper explores numerically the efficiency of $\lun$ minimization for the recovery of sparse signals from compressed sampling measurements in the noiseless case. Inspired by topological criteria for $\lun$-identifiability, a greedy algorithm computes sparse vectors that are difficult to recover by $\ell_1$-minimization. We evaluate numerically the theoretical analysis without resorting to Monte-Carlo sampling, which tends to avoid worst case scenarios. This allows one to challenge sparse recovery conditions based on polytope projection and on the restricted isometry property.
Subjects / KeywordsL1 minimization; sparsity; Compressed sensing
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