000087342 001__ 87342
000087342 005__ 20181203020430.0
000087342 0247_ $$2doi$$a10.1109/TIT.2005.860474
000087342 02470 $$2ISI$$a000234412500019
000087342 037__ $$aARTICLE
000087342 245__ $$aOn the exponential convergence of Matching Pursuits in quasi-incoherent dictionaries
000087342 269__ $$a2006
000087342 260__ $$c2006
000087342 336__ $$aJournal Articles
000087342 520__ $$aThe purpose of this paper is to extend results by Villemoes and Temlyakov about exponential convergence of Matching Pursuit with some structured dictionaries for ``simple'' functions in finite or infinite dimension. Our results are based on an extension of Tropp's results about Orthogonal Matching Pursuit in finite dimension, with the observation that it does not only work for OMP but also for MP. Our 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.
000087342 6531_ $$adictionary
000087342 6531_ $$aLTS2
000087342 6531_ $$amatching
000087342 6531_ $$anonlinear approximation
000087342 6531_ $$asparse representation
000087342 700__ $$aGribonval, R.
000087342 700__ $$g120906$$aVandergheynst, P.$$0240428
000087342 773__ $$j52$$tIEEE Transactions on Information Theory$$k1$$q255-261
000087342 909C0 $$xU10380$$0252392$$pLTS2
000087342 909CO $$pSTI$$particle$$ooai:infoscience.tind.io:87342
000087342 937__ $$aEPFL-ARTICLE-87342
000087342 970__ $$aGribonval2005_1367/LTS
000087342 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000087342 980__ $$aARTICLE