期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 24, 期 1, 页码 120-128出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2007.09.002
关键词
sparse representation; basis pursuit; matching pursuit; time-frequency dictionaries; wavelets; Wilson basis
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. (c) 2007 Elsevier Inc. All rights reserved.
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