对称多小波紧框架的参数化

Parameterizations of symmetric multiwavelet tight frames

酉扩展原理提供了一种很好地刻画和构造小波框架的方法。本文首先以对应于多小波框架的模矩阵和多相矩阵的形式,给出了m带多小波框架的对称特征,然后基于酉扩展原理和仿酉结构的因式分解,得到了构造具有特定性质的多小波框架的参数化方案。

The unitary extension principle provides a good way to characterize and construct framelets. This paper gives a characterization of symmetry of m-band multiwavelet frames in the form of modulation matrices and polyphase matrices. After that,based on the extension principle and the factorization of paraunitary structure,a scheme to construct multiwavelet frames with the desired properties is given.