The discrete wavelet transform for a symmetric-antisymmetric multiwavelet family on the interval

The Chui-Lian multiwavelet family of approximation order three is extended to serve as a basis for an orthogonal discrete multiwavelet transform on the interval. This requires, in addition to the original symmetric and antisymmetric pairs of scaling functions and wavelets, four new functions of each type at each edge of the interval, i.e., one more than required just to preserve the approximation order. The criteria are given that such edge functions must satisfy in order to allow multiresolution analysis of data sequences without special constraints on endpoint behavior or use of periodic boundary conditions, and a specific choice is examined in applications to both noiseless and noisy data. These are accomplished through the development of interval-basis extensions for both an earlier multiwavelet projection-based prefilter/postfilter combination and a multiwavelet vector thresholding algorithm.