小波去噪中噪声估计失真判别方法

Identification Method for Noise Estimation Distortion in Wavelet Denoising

研究小波阈值去噪时存在的噪声估计失真问题。当采用常见的阈值确定方法对含有较强高频分量的信号进行小波去噪时,小波分析的频带能量泄漏现象会导致噪声估计失真,从而使小波阈值去噪出现较大的偏差。从小波分解的d1细节层和d2细节层的相关性角度,揭示d2细节层频带能量泄漏对噪声估计影响的规律,提出根据d1、d2细节层的最大相关系数判别噪声估计失真的方法。最后,给出解决噪声估计失真的方法。实验表明,该方法可以很好地判别小波去噪中是否出现噪声估计失真,可以避免出现去噪后信号有用信息损失严重的问题。

When the signals containing some high frequency components are denoised by using the wavelet denoising with conventional threshold selection methods, the frequency-band energy leakage in wavelet analysis will lead to the distortion of the noise estimation, so that the wavelet threshold denoising may contain large errors. In this paper, the noise estimation distortion in the wavelet threshold denoising was studied. In view of the relevance between the d1 detail level and the d2 detail level, the influence of the frequency-band energy leakage of the d2 detail level on the noise estimation was analyzed. The identification method for noise estimation distortion was proposed by using the maximum correlation coefficient of the d1 detail level and the d2 detail level. Finally, the method of restraining the noise estimation distortion was given. The results of test show that the noise estimation distortion can be distinguished by using this method, and the trouble of the useful information missing in the wavelet denoising process can be avoided.