Optimal prefilters for the multiwavelet filter banks

This paper proposes a method to obtain optimal 2nd-order approximation preserving prefilters for a given orthogonal unbalanced multiwavelet basis. This procedure uses the prefilter construction introduced in Hardin et al., (1998). The prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. Using the DGHM multiwavelet with the obtained optimal prefilter, we find that quadratic input signals are annihilated by the high-pass portion of the filter bank at the first level of decomposition.