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On the exponential convergence of Matching Pursuits in quasi-incoherent dictionaries
Abstract : 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.
Keywords :
OMP
approximation error
exponential convergence
finite dimension
greedy algorithm
nonlinear approximation
orthogonal matching pursuit
quasiincoherent dictionary
sparse representation
stability property
approximation theory
greedy algorithms
image processing
iterative methods
numerical stability
sparse matrices
time-frequency analysis
Cited literature [25 references]
https://hal.inria.fr/inria-00544945
Contributor : Rémi Gribonval Connect in order to contact the contributor
Submitted on : Saturday, December 11, 2010 - 5:31:34 PM
Last modification on : Friday, February 4, 2022 - 3:18:27 AM
Long-term archiving on: : Saturday, March 12, 2011 - 2:25:17 AM
Contributor : Rémi Gribonval Connect in order to contact the contributor
Submitted on : Saturday, December 11, 2010 - 5:31:34 PM
Last modification on : Friday, February 4, 2022 - 3:18:27 AM
Long-term archiving on: : Saturday, March 12, 2011 - 2:25:17 AM
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