基于二进提升格式构造具有高阶消失矩的二进小波滤波器

Based on the Dyadic Lifting Scheme to Construct Dyadic Wavelet Filter with Higher-order Vanishing Moments

文章利用提升格式和对偶二进提升格式,分别构造出新的具有8阶高消失矩的提升二进小波滤波器和具有6阶高消失矩的对偶提升二进小波滤波器。第一步:对Mallat所构造的B-样条二进小波(r=1)进行拓展,通过大量的计算,反复实验,最后进行证明,可以得到构造新的B-样条二进小波的方法;第二步:运用上述构造二进小波的新方法,构造出新的B-样条二进小波(r=2)作为初始二进小波滤波器,再基于二进提升格式和对偶二进提升格式,分别进行三次提升,推导出具有有限长、线性相位、高阶消失矩的提升二进小波滤波器和对偶提升二进小波滤波器,而这些提升的二进小波滤波器并不能通过Sweldens提升格式进行计算获得,只能有本文所述的二进提升格式得到。

Article use lifting scheme and dual binary scheme, respectively constructs the new ascension has high 8 order disappear moment binary wavelet filter and high order 6 disappear moment of dual lifting binary wavelet filter. The first step：To construct Mallat B - spline dyadic wavelet （ r = 1） expand, through a lot of calculation, experiment repeatedly, finally proved that can get construct new B - spline dyadic wavelet method; The second step：using the new method of constructing binary wavelet, constructs the new B - spline dyadic wavelet （ r = 2） as the initial binary wavelet filter, and then based on the binary scheme and dual binary scheme, ascension for three times, respectively is deduced with limited length, linear phase, high order vanished moments of binary wavelet filter and dual lifting binary wavelet filter, and the ascension of the binary wavelet filter which are not avail？able through promotion Sweldens scheme to calculate, there can only be described in this article the binary scheme for ascension.