Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 52, Issue 1, Pages 255-261Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2005.860474
Keywords
dictionary; greedy algorithm; matching pursuit (MP); nonlinear approximation; sparse representation
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The purpose of this correspondence is to extend results by Villemoes and Temlyakov about exponential convergence of Matching Pursuit (MP) with some structured dictionaries for simple functions in finite or infinite dimension. The results are based on an extension of Tropp's results about Orthogonal Matching Pursuit (OMP) in finite dimension, with the observation that it does not only work for OMP but also for MP The main contribution is a detailed analysis of the approximation and stability properties of MP with quasi-incoherent dictionaries, and a bound on the number of steps sufficient to reach an error no larger than a penalization factor times the best m-term approximation error.
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