Construction of multi-wavelets from compactly supported refinable super functions

Abstract

In this work, a new method for constructing multi-wavelets with arbitrary approximation order is presented. The approach uses refinable super functions which enable the formulation of approximation order condition in terms of a generalized eigenvalue equation. The generalized left eigenvectors of the resulting finite down-sampled convolution matrix are recognized as the coefficients that enter the finite linear combination of multi-scaling functions that produce the desired super function. The method is demonstrated by constructing a specific class of multi-wavelets with approximation order 2, which includes Geronimo-Hardin-Massopust (GHM) multi-wavelet as one of its parameterized solutions. A new multi-wavelet, possessing approximation order three and multiplicity two with support [0, 2] and [0, 3] is also constructed. (C) 2003 Elsevier Science (USA). All rights reserved.