基于新的小波变换的去噪方法

A Denoising Method Based on New Wavelet Transforms

本文系统地分析了传统连续小波变换的缺陷。传统连续小波变换的逆变换中,积分变量是彼此独立的。只有当积分变量有联系时,相应的数值积分才具有高分辨特性,并且在逆变换中,积分变量出现在被积函数的分母上,这样会影响数值积分的精度,阻碍了连续小波变换的应用。为此构造了一种新型的连续小波变换,不论对积分变量如何剖分,任何一种数值积分方法都具有高分辨特性,且积分变量不出现在被积函数的分母上,进而给出了相应的数值解法。最后,给出了基于新型连续小波变换的滤波方法,对同时带有白噪声和脉冲噪声的信号进行处理。无需噪声的先验知识,就可以彻底地去除信号中白噪声和脉冲噪声,重建原有信号,与传统的小波去噪方法比较,可获取更高的信噪比。

The defects of the classical wavelet transforms are analyzed systemically. In the classical continuous wavelet inverse transform, the integral variables are independent. As the integral variables are dependent, the corresponding numeral integral has high resolution. The fact that the integral variable of the inverse transform appears in the denominator of integnmd reduces resolution of the numeral integral and blocks the application of them. So a new type of continuous wavelet transform is proposed. No matter what we discretize integral variables, any numeral integral has a high resolution, and the integral variable does not appear in the denominator of the integrand. In addition, the corresponding numerical method is obtained. Finally, a filter based on the new CWT is present. By dealing with the signals with white noise and outlier, the white noise and outlier in the signals could be completely wiped off and the original signals could be reconstructed without prior distribution of the noise, compared with other traditional wavelet denoising methods, the new CWT can achieve higher signal-to-noise ratio.