Beyond Coherence : Recovering Structured Time - Frequency Representations
نویسنده
چکیده
We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the Basis Pursuit and (Orthogonal) Matching Pursuit algorithms to recover a structured representation of an admissible signal. The sufficient conditions take into account the structure of the wavelet/Wilson dictionary and allow very large (even infinite) support sets to be recovered even though the dictionary is highly coherent. Key-words: sparse representation, overcomplete dictionary, matching pursuit, basis pursuit, time-frequency dictionaries, wavelets, Wilson basis, linear programming, greedy algorithm, , identifiability, inverse problem.
منابع مشابه
Universitet Beyond coherence : Recovering structured time - frequency represenatations
We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the Basis Pursuit and (Orthogonal) Matching Pursuit algorithms to recover a structured representation of an admis...
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