混沌信号的自适应阈值同步挤压小波变换消噪

针对同步挤压小波变换（SST）消噪过程中仅使用单一阈值的不足，对SST消噪时的幅度阈值进行了改进，提出了一种基于SST分层阈值的混沌信号消噪方法.首先，根据信号和噪声经SST分解后系数的分布模型，推导SST混沌去噪时幅度阈值权系数的均方误差计算公式；进而，根据均方误差最小准则，计算幅度阈值权系数的最优取值；最后，根据最优阈值权系数和噪声标准差，确定SST混沌去噪时的分层阈值.利用模拟混沌信号和实测月太阳黑子信号对所提方法进行了实验分析，实验结果表明，本文方法可较好地滤除混沌信号中的噪声，同时原始信号的内在混沌特性也能得到较大程度的恢复.与小波阈值法和集合经验模态分解（EEMD）消噪法相比，可获得更好的消噪效果.

Chaotic Signal De-noising Based on Adaptive Threshold Synchrosqueezed Wavelet Transform

For the lack of the single threshold denoising method of synchrosqueezed wavelet transform(SST),an improved denoising method for chaotic signal is proposed based on SST hierarchical threshold.Firstly,according to the distribution models of SST decomposition coefficients of the signal and the noise,the formula of mean square error of SST chaotic signal denoising is derived,which contains the threshold coefficients of amplitude.Then,the optimal threshold coefficients of amplitude is calculated based on the minimum mean square error criterion.Finally,the optimal hierarchical thresholds of SST chaotic denoising is determined according to the optimal threshold coefficients and the standard deviation of the noise.In the experiments,the denoising performance of the proposed method is tested by using the simulated chaotic signals and the measured monthly sunspot signals.The experimental results show that the proposed method can filter the noise of chaotic signal better,and the chaotic properties of the originals can be largely recovered.The proposed method can obtain better performance in the chaotic signal denoising than the classical wavelet transform threshold method and the EEMD denoising method.