Existence and generation of filter banks of general biorthogonal vector wavelets with finite support

In this paper, the notion of vector-valued multiresolution analysis and biorthogonal vector wavelets is introduced. The existence of finitely supported biorthogonal vector wavelets associated with a pair of biorthogonal finitely supported vector scaling functions is investigated. An algorithm for constructing a class of biorthogonal compactly supported vector wavelet functions is presented by using multiresolution analysis and matrix theory. The sufficient condition for the existence of multiple pseudoframes for subspaces of L²(R) is obtained.