Construction and Properties of Filter Banks of Vector-valued Scaling Functions

Wavelet analysis has become a popular subject in scientific research for twenty years. In this paper, the notion of vector-valued multiresolution analysis and biorthogonal vector-valued wavelets are introduced. The existence of biorthogonal finitely supported vector wavelets associated with a pair of biorthogonal finitely supported vector scaling functions is investigated. An algorithm for constructing a sort of biorthogonal finitely supported vector-valued wavelet functions is presented by using multire-solution analysis and unitary extension principle. The pyramid de-decomposition scheme is obtained. Relation to functional analysis is also obtained.