具有特定结构的离散型八进对称正交小波  

The Discrete Orthogonal Eight-Bank Wavelets with Symmetry and Specific Structure

作　　者：杨梦云 YANG Mengyun(School of Science,Shaoyang University,Shaoyang 422000,China;School of Information Science and Engineering,Central South University,Changsha 410083,China)

机构地区：[1]邵阳学院理学院,湖南邵阳422000 [2]中南大学信息科学与工程学院,湖南长沙410083

出　　处：《邵阳学院学报（自然科学版）》2018年第3期1-7,共7页Journal of Shaoyang University：Natural Science Edition

基　　金：湖南省教育厅一般项目(17C1434)

摘　　要：针对构造八进正交小波滤波器会遇到大量未知量的问题,结合低通滤波器系数和高通滤波器系数满足的正交条件,文章基于一种特定的数学结构,构造出了一类满足对称性或反对称性、具有高消失矩的八进正交小波滤波器。该小波类的七支高通滤波器只需由它的低通滤波器通过改变符号和位置来确定,因此在求解滤波器系数的过程中大大减少了未知量的个数,从而实现了快速计算。同时这类八进小波滤波器具有对称性或反对称性,可方便地将其自由度运用到应用背景中。In the process of constructing orthogonal eight-bank wavelet filters,a large number of unknown quantities are encountered,and the orthogonal conditions are satisfied by the low and high-pass filter coefficients.By using a specific structure,the symmetry or anti-symmetry eight-bank orthogonal wavelets with high vanishing moments were constructed.By changing the coefficient of symbols and position,the low-pass filters can generate another seven high-pass filters in this wavelet class.This construction brings a lot of convenience in calculation,which can be applied to the engineering background for using its free degrees.

关 键 词：八进正交小波 对称性 滤波器 消失矩 图像压缩 

分 类 号：O174.2[理学—数学]