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Near Best Tree Approximation

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Title: Near Best Tree Approximation
Author: Baraniuk, Richard G.; DeVore, Ronald A.; Kyriazis, George; Yu, Xiang Ming
Type: Journal Paper
Keywords: compression; n-term approximation; encoding; approximation classes
Citation: R. G. Baraniuk, R. A. DeVore, G. Kyriazis and X. M. Yu, "Near Best Tree Approximation," Advances in Computational Mathematics, vol. 16, pp. 357-373, 2002.
Abstract: Tree 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 n-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 L<sub>2</sub>, or in the case p not equal to 2, in the Besove spaces, which is close to (but not the same as) L<sub>p</sub>. 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.
Date Published: 2002-01-15

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  • ECE Publications [1034 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.