Near Best Tree Approximation

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dc.citation.bibtexNamearticleen_US
dc.citation.firstpage357en_US
dc.citation.journalTitleAdvances in Computational Mathematicsen_US
dc.citation.lastpage373en_US
dc.citation.volumeNumber16en_US
dc.contributor.authorBaraniuk, Richard G.en_US
dc.contributor.authorDeVore, Ronald A.en_US
dc.contributor.authorKyriazis, Georgeen_US
dc.contributor.authorYu, Xiang Mingen_US
dc.contributor.orgCenter for Multimedia Communications (http://cmc.rice.edu/)en_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T00:36:10Zen_US
dc.date.available2007-10-31T00:36:10Zen_US
dc.date.issued2002-01-15en_US
dc.date.modified2006-06-05en_US
dc.date.submitted2001-09-20en_US
dc.descriptionJournal Paperen_US
dc.description.abstractTree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar <i>n</i>-term wavelet approximation is that the wavelets appearing in teh appromant are required to align themselves in a certain connected tree structure. This makes their positions easy to encode. Previous work [CDGO], [CDDD] has established upper bounds for the error of tree approximation for certain (Besov) classes of functions. The present paper, in contrast, studies tree approximation of individual functions with the aim of characterizing those functions with a rpescribed approximation error. This accomplished in the case that the approximation error is measure in <i>L<sub>2</sub></i>, or in the case <i>p</i> not equal to 2, in the Besove spaces, which is close to (but not the same as) <i>L<sub>p</sub></i>. Our characterization of functions with a prescribed approximation order in these cases is given in terms of a certain maximal function applied to the wavelet coefficients.en_US
dc.description.sponsorshipOffice of Naval Researchen_US
dc.description.sponsorshipArmy Research Officeen_US
dc.description.sponsorshipNational Science Foundationen_US
dc.identifier.citationR. G. Baraniuk, R. A. DeVore, G. Kyriazis and X. M. Yu, "Near Best Tree Approximation," <i>Advances in Computational Mathematics,</i> vol. 16, 2002.en_US
dc.identifier.doihttp://dx.doi.org/10.1023/A:1014554317692en_US
dc.identifier.urihttps://hdl.handle.net/1911/19711en_US
dc.language.isoengen_US
dc.subjectcompressionen_US
dc.subjectn-term approximationen_US
dc.subjectencodingen_US
dc.subjectapproximation classesen_US
dc.subject.keywordcompressionen_US
dc.subject.keywordn-term approximationen_US
dc.subject.keywordencodingen_US
dc.subject.keywordapproximation classesen_US
dc.subject.otherWavelet based Signal/Image Processingen_US
dc.titleNear Best Tree Approximationen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
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