多尺度多重向量值双正交小波的构建算法与性质  

Constructive Algorithms and Properties for Multiple Vector-Valued Biorthogonal Wavelets with Multi-Scale

作　　者：宋亮[1] 张桂霞 程正兴[3] 

机构地区：[1]南阳理工学院数学与统计学院,河南南阳473004 [2]三门峡市教师进修学校数学教研室,河南三门峡472000 [3]西安交通大学数学与统计学院,陕西西安710049

出　　处：《数学的实践与认识》2016年第9期230-240,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61403298);陕西省自然科学基金(2015J1024)

摘　　要：研究多尺度多重向量值双正交小波的构建算法与性质.运用向量细分格式、矩阵理论和多重向量值多分辨分析,证明了与一对给定的多尺度多重向量值双正交尺度函数对应的多尺度多重向量值双正交小波函数的存在性.提出了紧支撑多尺度多重向量值双正交小波的构造算法.讨论了多尺度多重向量值小波包的性质,得到了多重向量值小波包的双正交公式与向量值小波包基.Existence and construction of biorthogonal multiple vector-valued wavelets with multi-scale are researched.We show that the existence of a pair of biorthogonal multiple vector-valued multi-scale scaling functions given guarantee the existence of pairs of associated biorthogonal multiple vector-valued poly-scale wavelet functions by means of vector subdivision scheme and matrix theory as well as multiple vector-valued multiresolution analysis.An algorithm for constructing a sort of compactly supported biorthogonal multiple vector-valued poly-scale wavelets.The properties of multiple vector-valued poly-scale wavelet packets are studied.The biorthogonality formulus for the multiple vector-valued poly-scale wavelet packets is established.The vector-valued wavelet packet bases are obtained.

关 键 词：向量细分格式 矩阵卷积 多重向量值小波 向量值小波包基 加细方程 

分 类 号：O174.2[理学—数学]