具有消失矩的对称紧支撑双正交多尺度分析的构造  

Construction of Compactly Supported Symmetrical Biorthonormal Multiresolution Analysis with Vanishing Moment

作　　者：梁茜[1,2] 丁宣浩[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林541004 [2]石家庄铁道学院四方学院,石家庄051132

出　　处：《数据采集与处理》2009年第3期386-390,共5页Journal of Data Acquisition and Processing

基　　金：国家自然科学基金(10871217)资助项目

摘　　要：依据Lawton条件,并结合传统的消失矩理论,研究了具有消失矩的对称紧支撑双正交多尺度分析的一般构造,同时列举滤波长度为8,消失矩为3的双正交多尺度分析(MRA,Multiresolution analysis)的构造实例。此方法通过求解一个方程组,可以得到含有自由变量的小波系数的关系式,再解决一个线性代数问题,求出自由变量所在的范围,即可构造出双正交多尺度分析。bior3.3小波就可以用此方法构造,且能构造出性质优于bior3.3的小波,将所构造出的小波实例用于图像和信号消噪,仿真结果表明该方法科学有效。Based on Lawton＇s condition and combined with traditional vanishing moment theory, the construction of compactly supported symmetrical biorthonormal multiresolution analysis（MRA） with vanishing moment is studied. An example about construction of biorthonormal MRA with filtering length 8 and vanishing moment 3 is given. A formula with free variable about wavelet coefficients is given by solving an equation. Then, by solving a linear algebra problem, the domains of filter coefficients for generating biorthonormal MRA are obtained. A bior3.3 wavelet is constructed with the method and its properties are better than that of bior3.3 wavelet. Some examples of the wavelet are applied to signal and figure denoise. Simulation results show that the method is effective.

关 键 词：双正交小波 多尺度分析 消失矩 特征根 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]