On Design of Multiwavelet Prefilters

A new approach for prefilter design/choice is proposed to improve the performance of multiwavelet transforms in data compression. The approach consists of two steps. In first step, a filter-bank is formed by the multiwavelet filter-bank and its prefilter. For perfect reconstruction (PR) in synthesis process, the new filter-bank is required to bring out no additive frequency spectrum distortion in analysis process. Some necessary conditions of prefilters can be educed from this requirement. In second step, for optimizing performance of multiwavelet transform in data compression, the new filter-bank is designed to maximize the proportion of frequency spectrum energy of low-pass filters in low-frequency band to total frequency spectrum energy. The proportion is treated as a criterion in designing and evaluating prefilters. The optimal prefilters for some general multiwavelets are devised from numerical calculation based on the necessary conditions and the criterion. Finally, results of some numerical experiments illustrate the proposed approach for prefilter design/choice is efficient and reliable.