摘要
基于仿酉矩阵的对称扩充方法,该文提出了一种尺度因子为3的紧支撑高维正交对称小波构造算法.即设φ(x)∈L^2(R^d)是尺度因子为3的紧支撑d维正交对称尺度函数,P(ξ)是它的两尺度符号,p_(0,v)(ξ)为P(ξ)的相位符号.首先提出一种向量的对称正交变换,应用对称正交变换对3~d维向量(p_(0,v)(ξ))_v,v∈E_d的分量进行对称化.通过仿酉矩阵的对称扩充,给出了3~d-1个紧支撑高维正交对称小波构造.这种方法构造的小波支撑不超过尺度函数的支撑.最后给出一个构造算例.
An algorithm for constructing the compactly supported multidimensional orthogonal symmetric wavelets with dilation factor 3 is provided based on paraunitary matrix symmetric extension.Namely,letφ{x）∈L^2（R^d） be ad dimensional compactly supported orthogonal scaling function with dilation factor 3;P（ξ） and（p（0,ν）（ξ）ν,ν∈E_d,respectively,be the mask symbol and the polyphase symbol ofφ（x）.Firstly,the authors propose a symmetric orthogonal transform of vectors,and take the symmetric orthogonal transform to（p（0,ν）（ξ）ν,ν∈Ed,then get a symmetric unit vector.Secondly,based on paraunitary matrix symmetric extension,3^d-1 compactly supported orthogonal symmetric wavelets associated withφ（x） are obtained.The support ofφν,ν∈Ed is not larger than that ofφ（x）.In addition,the algorithm can also be used to construct orthogonal wavelets with the dilation factor M（M≥3）.Finally,an example is given.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2010年第2期375-385,共11页
Acta Mathematica Scientia
基金
广东省自然科学基金(032038
05008289)
广东省自然科学博士基金(04300917)
汕头大学青年科研基金资助
关键词
正交对称变换
仿酉矩阵的对称扩充
正交小波
正交尺度函数
对称性
Orthogonal symmetric transform
Paraunitary matrix symmetric extension
Orthogonal wavelets
Orthogonal scaling function
Symmetry
