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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。
Recently, it has been proposed to construct wavelets by using the undetermined coefficient lifting scheme, and the resulting lifting scheme generally has four steps to be improved. Differently, this article uses a 5-step boost format to construct the wavelet. The result is a wavelet with very simple coefficients (especially in its ascending format). Its order of vanishing moments is as large as that of D9 / 7 wavelet, but the coefficients of the corresponding filters are simple fractions. In its ascending format, the denominator of all coefficients is a power of 2, and the numerator is 1. Only one 0 to 3 bit shift per step of the enhancement format is required. The wavelet approximates or surpasses the D9 / 7 wavelet in some mathematical properties, which will be verified by numerical experiments on image compression.