TITLE:
Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications
AUTHORS:
Lorella Fatone, Maria Cristina Recchioni, Francesco Zirilli
KEYWORDS:
Approximation Theory, Wavelet Bases, Kernel Sparsification, Image Compression
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.2,
February
25,
2011
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.