AM  Vol.2 No.2 , February 2011
Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications
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.
Cite this paper: nullL. Fatone, M. Recchioni and F. Zirilli, "Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications," Applied Mathematics, Vol. 2 No. 2, 2011, pp. 196-216. doi: 10.4236/am.2011.22022.

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