参数化的三带小波框架中的扩充矩阵的构造

Construction of an extension matrix for the parameterization of three-band wavelet frames

采用矩阵扩充的方法来解决参数化方法构造小波框架过程中系数矩阵是非方阵的问题。给出了三带小波紧框架的基本定义,并在酉扩张原理(UEP)的方法下对系数矩阵进行扩充,使其成为一个方阵,以数学的方法求得增列表达式,并在此基础上通过后续的对称变换,分解算法及参数化方法,最终构造出参数化的带有对称性质或反对称性质的三带小波框架。

This paper presents a matrix extension method to solve a problem when the coefficient matrix of parameterizations is not a square matrix.Some definitions of three-band tight wavelet frames are first given.Then the unitary extension principle（UEP） is used for the coefficient matrix extension,and a square matrix is obtained.The expression of the extension part can be calculated by mathematical methods.Based on the result,by the symmetry transformation,factorization and parameterizations,parameterizations of three-band wavelet frames with either symmetrical properties or antisymmetrical properties can be constructed.