Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters

Abstract

The aim of the paper is to construct a multiresolution analysis of L 2 (IR d) based on generalized kernels which are fundamental solutions of differential operators of the form m ℓ=1 (−∆+κ 2 ℓ I). We study its properties and provide a set of pre-wavelets associated with it, as well as the filters which are indispensable to perform decomposition and reconstruction of a given signal, being very useful in applied problems thanks to the presence of the tension parameters κ ℓ .