Shortest multi-wavelet matrix filters for refinable vector splines

Abstract

In multi-wavelet decomposition techniques for the analysis of a given vector-valued signal, it is desirable with respect to the computational efficiency of the associated algorithms that the low-pass and high-pass matrix filters sequences be as short as possible. By applying a multi-wavelet construction method based on the solving of a system of four matrix Laurent polynomial identities, and using as main building block a class of arbitrarily smooth refinable vector splines, we establish an explicitly formulated class of shortest possible associated matrix filter sequences for decomposition, as well as minimally supported spline multi-wavelets for these optimal filter sequences.