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一个新的带非常简单系数的双正交小波

周化雨1, 杨坦2, 关履泰1(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)

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。
关键词
A New Biorthogonal Wavelet with Very Simple Coefficients

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Abstract
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.
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