Construction of a class of compactly supported orthogonal vector-valued wavelets

In this paper, first we introduce vector-valued multiresolution analysis with dilation factor alpha >= 2 and orthogonal vector-valued wavelet. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelet is derived. Then, for a given L-length compactly supported orthogonal vector-valued wavelet system, by virtue of an s x s orthogonal real matrix M and an s x s symmetry idempotent real matrix H where M(I-s - H + He-in) is a unitary matrix for each eta is an element of R, we construct (L + 1)-length compactly supported orthogonal vector-valued wavelet system. Our method is of flexibility and easy to carry out. Finally, as an application we give an example. (c) 2006 Elsevier Ltd. All rights reserved.