小波包结点阈值自适应消噪法

Noisy signal decomposition based on wavelet packet

当噪声为时变的时候,传统的小波阈值消噪方法效果很有限:当采用软阈值消噪时,总体效果较好,但当含噪信号很不规则时显得过于光滑;当采用硬阈值消噪时,消噪效果不理想,信号含有明显的噪声。为克服上述缺陷,本文提出基于"自适应阈值消噪思想"的小波包结点阈值消噪法。首先,我们给出了小波包结点阈值的定义,这种阈值取法突破了高斯白噪声和平稳噪声的局限性;其次,我们提出了基于谱熵的噪声估计法用以替代传统的中值绝对值(MAD)噪声估计法,这种噪声估计方法与实际应用环境相符,适用于非平稳噪声和有色噪声。仿真实验证实,相比于常规小波消噪算法,结点阈值法和基于谱熵的噪声估计法在白噪声环境下具有较好的消噪效果。

The conventional wavelet thresholding methods based denoising algorithm are limited when the noise is non- stationary. Using the soft thresholding method , the denoised signal is too smooth to use when the noisy signal is very irregular. Using the hard thresholding method, the denoised signal still contains a lot of noise. So a new algorithm is proposed for denoising, adaptive wavelet packet is used for noisy signal decomposition. Node dependent thresholding is proposed and a method based on spectral entropy is applied to estimate the node noise. First, we propose node dependent thresholding for adaptation in non-stationary or colored noise. Next, we suggest a noise estimation method based on spectral entropy using histogram of intensity instead of estimation method based on median absolute deviation （MAD）. This algorithm is valid on white noise condition for comparison with the conventional wavelet thresholding methods.