A new prefilter design for discrete multiwavelet transforms

In conventional wavelet transforms, prefiltering 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 prefilters have appeared, but the existing prefilters are usually not orthogonal, which often causes problems in coding. Moreover, the condition on the prefilters was imposed based on the first-step discrete multiwavelet decomposition. We propose a new prefilter design that combines the ideas of the conventional wavelet transforms and multiwavelet transforms. The prefilters are orthogonal but nonmaximally decimated. They are derived from a very natural calculation 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-Massopust (1994) 2 wavelet transform and our new prefiltering is better than the one with Daubechies D₄ wavelet transform