多尺度双向向量值小波的构造与性质  

Construction and Properties for Two-direction Vector-valued Wavelets with Multi-scale

作　　者：陈清江[1] 王晓凤[2] 白娜[1] 魏冰蔗 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]河南城建学院数理学院,河南平顶山467036

出　　处：《应用数学》2015年第3期662-673,共12页Mathematica Applicata

基　　金：国家自然科学基金(61403298);陕西省教育厅专项科研基金(2013JK0564;12JK0868)

摘　　要：本文研究多尺度双向向量值正交小波的存在性、构造算法与性质.利用多分辨分析理论,时频分析方法与矩阵理论,给出紧支撑多尺度双向向量值正交小波的构造算法,得到多尺度双向向量值小波包的正交公式与向量值小波包基.推广了向量值正交小波的概念.In this paper, existence and construction as well as properties of orthogonal two-direction vector-valued wavelets with multi-scale are investigated. A construction algorithm for compactly supported orthogonal two-direction vector-valued wavelets is presented by virtue of the multi-resolution analysis and time-frequency method as well as matrix theory. The orthogonality formulas for two-direction vector-valued wavelet packets with multi-scale and vector-valued wavelet packet bases are obtained. The notion for vector-valued wavelets is generalized.

关 键 词：双向向量值尺度函数 双向向量值小波 向量值多分辨分析 面具函数 

分 类 号：O174.2[理学—数学]