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.

Prefiltering a given discrete signal has been shown to be an essential and necessary step in applications using unbalanced multiwavelets. In this paper, we develop two methods to obtain optimal second-order approximation preserving prefilters for a given orthogonal multiwavelet basis. These procedures use the prefilter construction introduced in part I of this paper. The first prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. The second one is achieved by minimizing the energy compaction ratio (ECR) of the wavelet coefficients for an experimentally determined average input spectrum. We use both methods to find prefilters for the cases of the DGHM and Chui-Lian (CL) multiwavelets. We then compare experimental results using these filters in an image compression scheme. Additionally, using the DGHM multiwavelet with the optimal prefilters from the first scheme, we find that quadratic input signals are annihilated by the high-pass portion of the filter bank at the first level of decomposition.