The description of the eminent multiple vector-valued univariate polyscale wavelet packs with finite support

In this paper, we introduce multiple vector-valued multiresolution analysis and orthogonal multiple vector-valued wavelet packets. A procedure of the construction of orthogonal multiple vector-valued wavelet packs is presented. The property of the multiple vector-valued wavelet packs has been characterized. In particular, a new orthogonal basis of L² (ℝ, ℂ^s×s) is drawn from these wavelet packs. The sufficient condition for the existence of multiple pseudoframes for subspaces of L²(R) is derived based on such a generalized multiresoution structure. The pyramid decomposition scheme is also obtained.