Chaotic Signal Denoising Based on Markov Model
Jianwei Fu · Jisuanji fangzhen · 2009
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.