Research On Noise Suppression For Chaotic Signals

Chaos is a seemingly random and irregular movement, happening in a deterministic system without random factors. Chaotic theory has promising applications in secure communication, image encryption, weak signal detection, biomedicine and so on. However, observed chaotic signals are often corrupted by noise, which not only makes it very difficult to compute Lyapunov exponent, correlation dimension, Kolmogorov entropy and other invariant system parameters but also destroys the intrinsic properties of chaotic attractors. This brings great difficulties to the application of chaotic theory. Therefore, it is significant to research on the noise suppression for chaotic signals. Focusing on the noise suppression technology for chaotic signals, this paper proposes solutions to problems with the existing methods of noise suppression for chaotic signals. It is composed of the following three parts:(1) In order to solve the parameter optimization issue of nonlinear adaptive denoising algorithm for chaotic signals, a parameter optimization nonlinear adaptive denoising algorithm for chaotic signals is proposed. Taking advantage of the difference in autocorrelation function of chaotic signals and noise, a new criterion is propsed. First, different window sizes are used for denoising noisy chaotic signals. Then, the residual autocorrelation degree of each window length is computed. Finally, the optimal window length is obtained by shrinking the window length corresponding to the minimum residual autocorrelation degree. Simulation results show that the parameter optimization performance of the original algorithm will degrade with the change of conditions, which influence the filter parameters and that the new algorithm can optimize the filter parameters automatically by the new criterion. So, the adaptivity of the new algorithm is better than the original algorithm, which makes it more appropriate for actual application.(2) The denoising algorithms for chaotic signals based on empirical mode decomposition(EMD) are studied systematically. In order to improve the denoising performance of partial reconstruction algorithm, a new algorithm is proposed. This algorithm decomposes the noisy chaotic signal by complete ensemble empirical mode decomposition(CEEMD) and determines the critical intrinsic mode function(IMF) by residual autocorrelation degree. Simulation results show that the denoising performance of the new algorithm is better than the original algorithm. In order to improve the adaptivity of interval thresholding algorithm, a new algorithm is proposed. This algorithm decomposes the noisy chaotic signal by CEEMD and denoises the IMF by interval thresholding. Simulation results show that the new algorithm, with no requirement of pretreatment, is more adaptable than the original algorithm and their donising performance is about the same. It is difficult to determine the threshold of mode cell in the interval thresholding algorithm, when it is used to denoise chaotic signals. In order to solve this problem, a zero-crossing scale thresholding adaptive denoising algorithm is proposed for chaotic signals based on CEEMD. First, the noisy chaotic signal is decomposed into the IMFs by CEEMD. Then, the zero-crossing scale thresholding denoising algorithm is used to denoise the IMFs with different thresholds. The optimal threshold is obtained by the Durbin–Watson criterion. With the optimal threshold, the final denoised chaotic signal is obtained. The proposed method solves effectively the problem mentioned above and the effectivity of this algorithm is verified by the experimental results.(3) A denoising algorithm is proposed for chaotic maps based on nonlocal means. The parameter setting of this algorithm is simple with good denoising performance, and the prior knowledge of system is not required. Simulation results show that this algorithm can denoise the noisy chaotic maps at different noise levels effectively and its denoising performance is better than the existing algorithms, including the phase space estimating projection method, the extended Kalman filter method and the unscented Kalman filter method.