具有高消失矩的3-进正交对称小波的构造(英文)  

Construction of Orthogonal 3-band Wavelets with Symmetry and High Vanishing Moments

作　　者：邹庆云[1,2] 王国秋[2] 曹前[1,2] 

机构地区：[1]湖南文理学院数学学院,湖南常德415000 [2]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《应用数学》2014年第1期100-106,共7页Mathematica Applicata

基　　金：Supported by the National Science Foundation of China(11171103);the ScienceFoundation of the Hunan Education Office(13C624,13C621)

摘　　要：本文给出一类具有高消失矩的对称3-进正交小波的构造.首先通过解非线性方程组构造出高消失矩的尺度函数.其次,基于矩阵扩充的方法,我们给出新的定理和算法.相应的关于原点对称/反对称的小波由我们提出的方法构造,并且,该方法便于计算机程序化实现.最后,我们通过3个实例来验证相关的结论,该类小波为应用提供了好的选择.The 3-band orthogonal wavelets with compact supported, symmetry, perfect reconstruction and high vanishing moments are constructed. A simple method is given to construct the scaling function with high vanishing moments by solving nonlinear equations. Two corresponding orthogonal wavelets,one is symmetric and the other is antisymmetric to origin, are constructed explicitly hy providing a step-by-step algorithm. Moreover,this algorithm is easily implemented by computer program. Several examples are provided to illustate the proposed algorithm and results in this paper.

关 键 词：正交小波 对称性 矩阵扩充 罗朗多项式 消失矩 

分 类 号：O174.2[理学—数学]