基于Laplace分布的非下采样小波包脉冲星信号消噪

Pulsar signal denoising method based on Laplace distribution in nosubsampled wavelet packet domain

为了提高脉冲星信号的去噪效果,提出了一种基于非下采样小波包(NWP)分解的局部Laplace模型消噪方法。首先对真实脉冲星信号进行NWP分解,统计真实脉冲星信号NWP系数的分布特性,建立真实脉冲星信号小波包系数的Laplace分布模型;然后在Laplace先验概率分布的基础上,根据最大后验概率(MAP)估计准则,利用含噪脉冲星信号的小波包系数对真实脉冲星信号的小波包系数进行有效估算;最后对估算出的小波包系数进行NWP重构,得到消噪后的脉冲星信号。采用不同的脉冲星信号进行实验分析的结果表明,与经典的基于高斯分布的非下采样小波(NSW)消噪和NWP消噪相比,本文方法可以更有效地去除噪声,同时更好地保留信号中的微脉冲等细节信息,在信噪比(SNR)、均方根误差(RMSE)、相关系数(CC)和峰值相对误差(REPV)等都有较好的改善。

To improve the denoising effect of pulsar signal, a new method is proposed in undeeimated wavelet packet domain based on local Laplace prior model. First,the undecimated wavelet packet coeffi- cients distribution characteristics of the true noise-free pulsar signal are counted,and the Laplace proba- bility density function model of the true signal wavelet packet coefficients is established. Then, the de- nosied wavelet packet coefficients are estimated by using the noisy pulsar wavelet coefficients based on maximum a posteriori （MAP） criterion. Finally, the denoised pulsar signal is obtained by nosubsampled wavelet packet reconstruction of the estimated coefficients. The experimental results show that the pro- posed method can get better denosing effect than the nosubsampled wavelet method and the nosubsam- pled wavelet packet method based on Gaussian distribution, which can more better remove the noise of pulsar signal and more effectively preserve the micro-pulse detail information. Moreover, the proposed method has a better improvement in signal-to-noie （SNR）, root mean square error, correlation coefficient and peak relative error, etc.