Multiwavelet prefilters - Part II: Optimal orthogonal prefilters

Prefiltering a given discrete signal has been shown to be an essential and necessary step in applications using unbalanced multiwavelets. In this pape r, we develop two methods to obtain optimal second-order approximation pres erving prefilters for a given orthogonal multiwavelet basis. These procedur es use the prefilter construction introduced in part I of this paper [5]. T he first prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. The second one is achieve d by minimizing the energy compaction ratio (ECR) of the wavelet coefficien ts for an experimentally determined average input spectrum. We use both met hods to find prefilters for the cases of the DGHM and Chui-Lian (CL) multiw avelets. We then compare experimental results using these filters in an ima ge compression scheme. Additionally, using the DGHM multiwavelet with the o ptimal prefilters from the first scheme, we find that quadratic input signa ls are annihilated by the high-pass portion of filter bank at the first lev el of decomposition.