000087067 001__ 87067
000087067 005__ 20190316233746.0
000087067 037__ $$aREP_WORK
000087067 245__ $$aOn the Use of A Priori Information for Sparse Signal Approximations
000087067 269__ $$a2004
000087067 260__ $$c2004$$aEcublens
000087067 336__ $$aReports
000087067 520__ $$aThis report is the extension to the case of sparse approximations of our previous study on the effects of introducing a priori knowledge to solve the recovery of sparse representations when overcomplete dictionaries are used. Greedy algorithms and Basis Pursuit Denoising are considered in this work. Theoretical results show how the use of "reliable" a priori information (which in this work appears under the form of weights) can improve the performances of these methods. In particular, we generalize the sufficient conditions established by Tropp and Gribonval & Vandergheynst, that guarantee the retrieval of the sparsest solution, to the case where a priori information is used. We prove how the use of prior models at the signal decomposition stage influences these sufficient conditions. The results found in this work reduce to the classical case of Tropp and Gribonval & Vandergheynst when no a priori information about the signal is available. Finally, examples validate and illustrate the theoretical results. Finally, examples validate and illustrate theoretical results.
000087067 6531_ $$aA Priori Knowledge
000087067 6531_ $$aBasis Pursuit
000087067 6531_ $$aGreedy Algorithms
000087067 6531_ $$aLTS2
000087067 6531_ $$aMatching Pursuit
000087067 6531_ $$aRedundant Dictionaries
000087067 6531_ $$aRelaxation Algorithms
000087067 6531_ $$aSparse Approximations
000087067 6531_ $$aSparse Representations
000087067 6531_ $$aWeighted Basis Pursuit
000087067 6531_ $$aWeighted Matching Pursuit
000087067 700__ $$0241064$$g134131$$aDivorra Escoda, O.
000087067 700__ $$0241529$$g141038$$aGranai, L.
000087067 700__ $$aVandergheynst, P.$$g120906$$0240428
000087067 8564_ $$uhttps://infoscience.epfl.ch/record/87067/files/Divorra_Escoda2004_1166.pdf$$zn/a$$s436491
000087067 909C0 $$xU10380$$0252392$$pLTS2
000087067 909CO $$qGLOBAL_SET$$pSTI$$ooai:infoscience.tind.io:87067$$preport
000087067 937__ $$aEPFL-REPORT-87067
000087067 970__ $$aDivorraEscoda2004_1166/LTS
000087067 973__ $$sPUBLISHED$$aEPFL
000087067 980__ $$aREPORT