A new prefilter design for discrete multiwavelet transforms

In conventional wavelet transforms, preflltering is not necessary due to the lowpass property of a scaling function. This is no longer true for multiwavelet transforms. A few research papers on the design of prefllters have appeared recently. However, the existing prefllters are usually not orthogonal, which often causes problems in coding. Moreover, the condition on the prefllters was imposed based on the firststep discrete multiwavelet decomposition. In this paper, we propose a new prefilter design that combines the ideas of the conventional wavelet transforms and multiwavelet transforms. The prefilters are orthogonal but nonmaxlmally decimated. They come from a very natural derivation of calculations of multiwavelet transform coefficients. In this new prefilter design, multiple step discrete multiwavelet decomposition is taken into account. Our numerical examples (by taking care of the redundant prefiltering) indicate that the energy compaction ratio with the Geronimo, Hardin, and Massopust 2 wavelet transform and our new prefiltering is better than the one with Daubechies 04 wavelet transform.