一类矩阵伸缩框架小波包的构造  

Construction of Framelet Packets with Dilation Matrix

作　　者：徐美玉[1] 姚怡[2] 鲁大勇[1,3] 

机构地区：[1]河南大学数学与统计学院,河南开封475004 [2]黄河水利职业技术学院基础部,河南开封475001 [3]河南大学应用数学研究所,河南开封475004

出　　处：《河南大学学报（自然科学版）》2016年第4期500-504,共5页Journal of Henan University:Natural Science

基　　金：国家自然科学基金(61471410);河南省教育厅科技攻关项目(13A110072);河南省科技厅项目(122300410381)

摘　　要：基于正交小波基的小波包在理论及应用上已经得到广泛的研究,但是对框架小波包的研究甚少.通过框架小波包,不但可以根据信号的特征选取不同的小波框架,而且还可以对信号的不同频率带进行分析和处理.Lu和Fan从Ron和Shen提出的酉延拓原理出发,构造出L^2(R^d)的一类具有2Id-伸缩的紧框架小波包.本文从Ron和Shen提出的酉延拓原理出发,利用Daubechies给出的分裂算法,将上述2Id-伸缩矩阵的结果推广到一般伸缩矩阵,给出了一类具有矩阵伸缩的框架小波包的构造方案,并利用该构造方案,构造出L^2(R^d)的一类框架小波包.Wavelet packets based on orthonormal wavelet bases have been well studied in theory and applications, but the study of framelet packets has been less involved. According to the character of the signals, we can not only choose different wavelet frames using framelet packets, but also analyze and process the signal with different frequency bands. Recently, Lu and Fan constructed a class of tight framelet packets with 2Id-dilation for L^2 （R^d ） from the unitary extension principles given by Ron and Shen. In this paper we extend the result to a general dilation matrix, and exploit splitting trick given by Daubechies, and present a method with which we can construct framelet packets with a general dilation matrix for L^2 （R^d） from the unitary extension principles given by Ron and Shen.

关 键 词：框架小波包 延拓原理 小波框架 伸缩矩阵 

分 类 号：O174.2[理学—数学]