Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications

Lorella Fatone, Maria Cristina Recchioni, Francesco Zirilli

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DOI: 10.4236/am.2011.22022                

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.

Keywords

Approximation Theory, Wavelet Bases, Kernel Sparsification, Image Compression

Conflicts of Interest

The authors declare no conflicts of interest.

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