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Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications
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Applied Mathematics·Volume 02 (2011)·Pages 196–216·Published 25 February 2011·DOI10.4236/am.2011.22022
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Abstract
We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases; in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.
KeywordsApproximation TheoryWavelet BasesKernel SparsificationImage Compression
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