基于白化检验和3?? 准则的小波阈值去噪算法

基于小波变换的阈值去噪法是去除数字信号中自噪声的有效算法。其中，分解层数、门限阈值以及阈值函数的选取是关键。本文分析了白噪声和有用信号的小波变换系数的特点，在此基础上提出了一种分解层数的自适应确定方法以及一种基于3σ准则的各层小波空问阈值的选取方法，并结合硬阈值和软阈值方法各自的优缺点，提出了一种改进的小波系数阈值估计的模型。仿真结果表明，该方法具有较好的去噪效果，尤其适用于强噪声背景下弱信号的检测。

Adaptive Wavelet Thresholding Denoising Algorithm Based on White Noise Detection and 3σ Rule

Threshold de-noising method based on wavelet transform is an efficient method to reduce the white noise in the digital signal. In this method, the determination of the threshold , the decomposition order and the threshold estimation model are three key problems that need to be solved. The characteristics of the wavelet coefficients of useful signal and white noise are analyzed. A new method is proposed to determine the decomposition order adaptively, and a novel method based on 3a rule is brought forward to determine the threshold of wavelet space of each order. Furthermore, a proved threshold estimation model of wavelet coefficients is proposed, which combines qualities of hard-thresholding and soft-thresholding models. Simulation results show that the method proposed has good performance of de-noising, and is especially used to detect weak signal from strong noise.