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• W1566625883 abstract "A series of recent results shows that if a signal admits a sufficiently sparse representation (in terms of the number of nonzero coefficients) in an “incoherent” dictionary, this solution is unique and can be recovered as the unique solution of a linear programming problem. We generalize these results to a large class of sparsity measures which includes the ℓp-sparsity measures for 0 ≤ p ≤ 1. We give sufficient conditions on a signal such that the simple solution of a linear programming problem simultaneously solves all the non-convex (and generally hard combinatorial) problems of sparsest representation w.r.t. arbitrary admissible sparsity measures. Our results should have a practical impact on source separation methods based on sparse decompositions, since they indicate that a large class of sparse priors can be efficiently replaced with a Laplacian prior without changing the resulting solution." @default.
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• W1566625883 date "2004-01-01" @default.
• W1566625883 modified "2023-09-24" @default.
• W1566625883 title "On the Strong Uniqueness of Highly Sparse Representations from Redundant Dictionaries" @default.
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• W1566625883 doi "https://doi.org/10.1007/978-3-540-30110-3_26" @default.
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