@inproceedings{bc9c0e000c9011dcb676000ea68e967b,

title = "On the strong uniqueness of highly sparse representations from redundant dictionaries",

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 l^p-sparsity measures for 0 \leq p \leq 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 respresentation 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 solutionA 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 l^p-sparsity measures for 0 \leq p \leq 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 respresentation 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",

author = "R{\'e}mi Gribonval and Morten Nielsen",

year = "2004",

language = "English",

isbn = "3540230564",

series = "Lecture Notes In Artificial Intelligence",

publisher = "IEEE Computer Society Press",

number = "3195",

pages = "201--208",

booktitle = "Independent Component Analysis and Blind Signal Separation",

address = "United States",

note = "On the strong uniqueness of highly sparse representations from redundant dictionaries ; Conference date: 19-05-2010",

}