Implementation of discrete vector-valued wavelet transforms

In this paper the discrete implementation of orthogonal multiwavelet transforms based on two scaling functions is discussed. In contrary to one scaling function (single-wavelets) using several scaling functions offers degrees of freedom that can be used to design orthogonal and symmetric, compactly supported wavelets. The discrete implementation of these vector-valued transformations can be executed by a wavelet-like transform using different stages of the filterbank. How to design these particular stages of the filterbank is discussed in this paper. Alternatively, it is shown how to take advantage of the degrees of freedom in designing the two scaling functions in order to construct multiwavelet systems with identical stages