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Optimally sparse image approximation by adaptive linear splines over anisotropic triangulations.
In: Proceedings (International Conference on Sampling Theory and Applications, SampTA 2015, 25-29 May 2015, Washington, USA). 2015. 463-467
Anisotropic triangulations provide efficient methods for sparse image representations. In previous work, we have proposed a locally adaptive algorithm for sparse image approximation, adaptive thinning, which relies on linear splines over anisotropic Delaunay triangulations. In this contribution, we address theoretical and practical aspects concerning image approximation by linear splines over anisotropic conformal triangulations. Our discussion includes asymptotically optimal N-term approximations on relevant classes of target functions, such as horizon functions across α Hölder smooth boundaries and regular functions of Wα, p regularity, for α > 2/p-1. Moreover, we demonstrate the good performance of our adaptive thinning algorithm by numerical examples and comparisons.
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Publication type Article: Conference contribution
Conference Title International Conference on Sampling Theory and Applications, SampTA 2015
Conference Date 25-29 May 2015
Conference Location Washington, USA
Proceedings Title Proceedings
Quellenangaben Pages: 463-467
Institute(s) Institute of Computational Biology (ICB)