高阶消失矩的二进小波滤波器的构造方法

Constructed Method of Dyadic Wavelet Filter of Higher-order Vanishing Moments

文中在二进提升格式的基础上,结合消失矩的条件和小波的相关理论,推导出一种构造新的具有高阶消失矩的二进小波滤波器的方法。首先,对Mallat提出的B-样条二进小波进行拓展,推导出构造新的B-样条二进小波滤波器方法;然后,在二进提升格式的基础上,以r=1,m=2的B-样条二进小波滤波器作为初始二进小波滤波器,经过多次提升和大量计算,构造出新的具有7阶消失矩的二进小波滤波器;最后,再以对偶二进提升格式为基础,选择合适的自由参数,对初始二进小波重构高通滤波器进行三次提升,推导出具有紧支集、线性相位、7阶消失矩的对偶提升二进小波滤波器。

Based on the dyadic lifting scheme, combined with the condition of vanishing moments and related wavelet theory, deduce a new two constructor method has higher-order moments vanish into the wavelet filter. First, B-spline dyadic wavelet proposed by Mallat is expanded into new methods to derive two wavelet filter structure B-spline. Then,based on binary format, with r = 1, m = 2 B-spline dyadic wavelet filter as the initial dyadic wavelet filter, after repeated lifting and a lot of calculations, construct a new binary wavelet filter with 7 vanishing moments. Finally ,based on the dual binary format ascension, select the appropriate freedom parameters for the three lift- ing to initial dyadic wavelet reconstruction high-pass filter, deducing lifting dyadic wavelet filters with compact support, linear phase, dual lifting 7-order vanishing moments.