Application of Multiwavelets to Signal Compression and Denoising

This paper investigates the emerging notion of multiwavelets in the context of multirate filter banks, and applies a multiwavelet system to image coding and signal denoising. Multiwavelets are of interest because their constituent filters can be simultaneously symmetric and orthogonal (this combination is impossible for 2-band PR-QMFs), and because one can obtain higher orders of approximation (more vanishing wavelet moments) for a given filter length. We develop symmetric extension methods for finitelength signals under multiwavelet filtering. Techniques are then presented for preand post-processing one-dimensional signals in order to effectively exploit multiwavelet structures. Finally, we employ these new tools and compare their performance with Daubechies’ scalar wavelets.