Explicit construction of symmetric compactly supported biorthogonal multiwavelets via group transformations
Explicit construction of symmetric compactly supported biorthogonal multiwavelets via group transformations
复制标题
DOI：
10.1016/j.cam.2012.11.018
复制
发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
Y. Cen;L. Cen;Xiao-Fang Chen;Z. Miao
中科院分区：
文献类型：
--
作者：
Y. Cen;L. Cen;Xiao-Fang Chen;Z. Miao
多尺度向量的多相矩阵扩张是构造紧支撑双正交多小波的基本方法。利用Laurent多项式环上的幺模群，研究了多尺度向量的多相矩阵的标准形以及满足PR条件的矩阵方程解的一些性质.在具有相同对称中心和不同对称中心的多尺度向量的多相矩阵的标准形下，可以得到由多尺度向量的多相矩阵表示的显式对称延拓公式.由此，提出了一种构造重数为2的对称紧支撑双正交多小波的新方法。最后，给出了几个例子来验证我们所提出的方法。
Polyphase matrix extension of multiscaling vectors is a fundamental approach for the construction of compactly supported biorthogonal multiwavelets. In this paper, canonical form of polyphase matrices of multiscaling vectors and some properties of solutions satisfying the matrix equation of PR condition are studied through unimodular groups over the Laurent polynomial ring. Under the canonical form of polyphase matrices of multiscaling vectors with the same symmetric center and different symmetric centers, explicit symmetric extension formulas expressed by the polyphase matrices of multiscaling vectors can be obtained. As a result, a novel approach for the construction of symmetric compactly supported biorthogonal multiwavelets with multiplicity 2 is proposed. Finally, several examples are given for verification of our proposed approach.