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Demaret, L. ; Iske, A.*

Optimal N-term approximation by linear splines over anisotropic Delaunay triangulations.

Math. Comput. 84, 1241-1264 (2015)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
Anisotropic triangulations provide efficient geometrical methods for sparse representations of bivariate functions from discrete data, in particular from image data. In previous work, we have proposed a locally adaptive method for efficient image approximation, called adaptive thinning, which relies on linear splines over anisotropic Delaunay triangulations. In this paper, we prove asymptotically optimal -term approximation rates for linear splines over anisotropic Delaunay triangulations, where our analysis applies to relevant classes of target functions: (a) piecewise linear horizon functions across -Hölder smooth boundaries, (b) functions of regularity, where , (c) piecewise regular horizon functions of regularity, where .
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Publication type Article: Journal article
Document type Scientific Article
Keywords Image Compression; Contourlet Transform; Wavelets; Representation
ISSN (print) / ISBN 0025-5718
e-ISSN 1088-6842
Quellenangaben Volume: 84, Issue: 293, Pages: 1241-1264 Article Number: , Supplement: ,
Publisher American Mathematical Society (AMS)
Reviewing status Peer reviewed