基于小波包变换的一种降噪算法

Denoising algorithm based on wavelet packet transform

白噪声的方差和幅值随着小波变换尺度的增加会逐渐减小 ,而信号的方差和幅值与小波变换的尺度变化无关。因此 ,文章提出一种以小波包能量为基础 ,以降低原始信号与降噪后信号之间的均方误差 (MSE)为目标的基于小波包的降噪算法 ,并与传统的 Donoho的硬阈值降噪算法作了比较。仿真结果表明 ,该算法可以有效去除白噪声干扰 ,并且明显优于传统的 Donoho的硬阈值降噪算法。

The variance and amplitude of the white noise decrease with the increase in the scale of the wavelet transform, but the variance and amplitude of a specific signal bear no relation to the wavelet transform scale. A new denoising algorithm based on wavelet packet transform is presented. It is aimed to reduce the mean square error(MSE) between the reconstructed signal and the original signal. Theoretical analysis and simulation results show that this algorithm has an obvious advantage over the traditional threshold based algorithm proposed by Donoho.