000087051 001__ 87051
000087051 005__ 20190316233746.0
000087051 037__ $$aREP_WORK
000087051 245__ $$aTree-Based Pursuit
000087051 269__ $$a2004
000087051 260__ $$c2004$$aEcublens
000087051 336__ $$aReports
000087051 500__ $$aITS
000087051 520__ $$aBuilding good sparse approximations of functions is one of the major themes in approximation theory. When applied to signals, images or any kind of data, it allows to deal with basic building blocks that essentially synthesize all the information at hand. It is known since the early successes of wavelet analysis that sparse expansions very often result in efficient algorithms for characterizing signals in noise or even for analyzing and compressing signals. The very strong links between approximation theory and computational harmonic analysis on one hand and data processing on the other hand, resulted in fruitful crossfertilizations over the last decade. This paper proposes to create a tree structure from an arbitrary dictionary of functions. Due to a hierarchical classification of the original data, an important part of the redundancy is intrinsically hold by the structure that represents whole bunch of highly correlated atoms by an unique element. A pursuit algorithm taking advantage of this structure is proposed. It consists in finding the best path through the tree. It presents the important advantage of being much faster than a classical Matching Pursuit. The proposed method reduces the dimensionality of the problems without losing important information for the problem at hand; it only minimally degrades the quality of approximation. The performance of the proposed algorithm are demonstrated in the context of image representation.
000087051 6531_ $$aLTS2
000087051 6531_ $$aLTS4
000087051 700__ $$0241006$$g114569$$aJost, P.
000087051 700__ $$0240428$$g120906$$aVandergheynst, P.
000087051 700__ $$aFrossard, P.$$g101475$$0241061
000087051 8564_ $$uhttps://infoscience.epfl.ch/record/87051/files/Jost2004_894.pdf$$zn/a$$s217135
000087051 909C0 $$xU10380$$0252392$$pLTS2
000087051 909C0 $$pLTS4$$xU10851$$0252393
000087051 909CO $$qGLOBAL_SET$$pSTI$$preport$$ooai:infoscience.tind.io:87051
000087051 937__ $$aEPFL-REPORT-87051
000087051 970__ $$aJost2004_894/LTS
000087051 973__ $$sPUBLISHED$$aEPFL
000087051 980__ $$aREPORT