An algorithm for constructing symmetric orthogonal multiwavelets by matrix symmetric extension

摘要

Symmetric extensions of paraunitary matrix is studied. Starting from a given m-band compactly supported orthogonal multiscaling function with some symmetric property, the problem to construct a corresponding m-band multiwavelet which have the symmetric property can be reduced to the symmetric paraunitary extension of a given matrix. It can be shown that such matrix extension is always solvable and an algorithmic approach to solve the symmetric paraunitary extension problem is presented. This leads to a practical method for the construction of compactly supported symmetric orthogonal multiwavelets from a given multiscaling functions with an arbitrary integer dilation factor m>1. As an application, some examples are given, in particular, the well known Chui–Lian multiwavelets is recovered via the method.