混沌信号的马尔可夫模型降噪

Chaotic Signal Denoising Based on Markov Model

基于马尔可夫模型的思想,提出了一种混沌信号的小波域统计降噪方法。利用对偶树复小波对信号进行小波分解,保留最高尺度上的尺度系数不变,对分解后的高频小波系数建立隐马尔可夫树模型。采用期望最大化算法估计该模型的参数,结合经验贝叶斯方法估计源信号的小波系数,再用对偶树复小波逆变换得到降噪后的混沌信号。该模型具有近似平移不变性,计算复杂度小且能够捕获小波系数邻域的统计特征。仿真中分别对叠加不同强度高斯噪声的Lorenz混沌信号及实测远红外激光器产生的混沌信号进行了研究。结果表明了该方法的有效性,且能够较好地校正相空间中点的位置,逼近真实的混沌吸引子轨迹。

A chaotic signal statistical denoising method in wavelet domain was proposed based on the idea of Markov model. The signal was decomposed by dual-tree complex wavelet. The wavelet coefficients as hidden Markov trees model was modeled while keeping the highest scale coefficients unchanged. Efficient Expectation Maximization algorithm was developed for fitting the hidden Markov trees model to wavelet coefficients. Empirical Bayesian method was used to estimate source signal wavelet coefficients. And using dual-tree complex wavelet inverse transform, the denoised chaotic signal could be got. The model is nearly shift invariant and can exploit the local statistics of wavelet coefficients at a low computational complexity. Both the chaotic signal generated by Lorenz map with different level Gaussian noise and the data generated by far-infrared laser were respectively applied for noise reduction using this method. The numerical experiments results show that the proposed method is efficient. It can better correct the position of data points in phase space and approximate the real chaotic attractor trajectories more closely.