Matrix Spectral Factorization for SA4 Multiwavelet

TL;DR

This paper presents a novel approach to matrix spectral factorization for multiwavelet construction, introducing regularization techniques and deriving orthogonal multiwavelet functions for SA4 multiwavelets.

Contribution

It develops a regularization method for Bauer's matrix spectral factorization and constructs orthogonal multiwavelet functions using QR decomposition.

Findings

Achieved approximate and exact orthogonal SA4 multiscaling functions

Derived orthogonal multiwavelet functions from spectral factors

Enhanced multiwavelet construction methods

Abstract

In this paper, we investigate Bauer's method for the matrix spectral factorization of an r-channel matrix product filter which is a halfband autocorrelation matrix. We regularize the resulting matrix spectral factors by an averaging approach and by multiplication by a unitary matrix. This leads to the approximate and exact orthogonal SA4 multiscaling functions. We also find the corresponding orthogonal multiwavelet functions, based on the QR decomposition.