一个新的带非常简单系数的双正交小波(英文)  

A New Biorthogonal Wavelet with Very Simple Coefficients

作　　者：周化雨[1] 杨坦[2] 关履泰[1] 

机构地区：[1]中山大学科学计算与计算机应用系,广州510275 [2]华南师范大学数学科学学院,广州510631

出　　处：《中国图象图形学报》2007年第7期1189-1193,共5页Journal of Image and Graphics

基　　金：国家自然科学基金项目(60475042);广东省自然科学基金项目(036608)

摘　　要：近来,通过带待定系数提升格式构造小波已经被提出,构造出的提升格式一般有4步提升。不同地是,本文使用5步提升格式来构造小波。最终获得一个带非常简单系数(特别是在其提升格式中)的小波。它的消失矩阶数与D9/7小波一样大,但相应滤波器的系数都是简单分数。在它的提升格式中,所有系数的分母是2的幂次,并且分子为1。提升格式的每一步只需要一个0到3位的位移。此小波在某些数学性质上接近或超过了D9/7小波,这将被之后的图像压缩的数值实验所验证。Constructing wavelets via the lifting scheme with indeterminate coefficient has been proposed recently. The constructed lifting schemes generally have four steps. Differently we use the five-step lifting scheme to construct wavelet. Finally, we obtain a wavelet with very simple coefficients especially in its lifting scheme. Its order of vanishing moments is the same with that of D9/7 wavelet, but the coefficients of the corresponding filters are simple fractions. In its lifting scheme, the denominators of all coefficients are the power of 2 and the numerators are 1. Every step of the lifting algorithm only needs a shift operation with 0 to 3 bits. This wavelet approaches or exxceeds D9/7 wavelet in some mathematical properties, which will be verified in the numerical experiments of image compressions.

关 键 词：提升格式 消失矩 双正交小波 

分 类 号：TN919.81[电子电信—通信与信息系统]