An adaptive denoising algorithm for chaotic signals based on collaborative filtering

Chaos is a seemingly random and irregular movement, happening in a deterministic system without random factors. Chaotic theory has promising applications in various areas (e.g., communication, image encryption, geophysics, weak signal detection). However, observed chaotic signals are often contaminated by noise. The presence of noise hinders the chaos theory from being applied to related fields. Therefore, it is important to develop a new method of suppressing the noise of the chaotic signals. Recently, the denoising algorithm for chaotic signals based on collaborative filtering was proposed. Its denoising performance is better than those of the existing denoising algorithms for chaotic signals. The denoising algorithm for chaotic signals based on collaborative filtering makes full use of the self-similar structural feature of chaotic signals. However, in the parameter optimization issue of the denoising algorithm, the selection of the filter parameters is affected by signal characteristic, sampling frequency and noise level. In order to improve the adaptivity of the denoising algorithm, a criterion for selecting the optimal filter parameters is proposed based on permutation entropy in this paper. The permutation entropy can effectively measure the complexity of time series. It has been widely applied to physical, medical, engineering, and economic sciences. According to the difference among the permutation entropies of chaotic signals at different noise levels, first, different filter parameters are used for denoising noisy chaotic signals. Then, the permutation entropy of the reconstructed chaotic signal corresponding to each of filter parameters is computed. Finally, the permutation entropies of the reconstructed chaotic signals are compared with each other, and the filter parameter corresponding to the minimum permutation entropy is selected as an optimal filter parameter. The selections of the filter parameters are analyzed in the cases of different signal characteristics, different sampling frequencies and different noise levels. Simulation results show that this criterion can automatically optimize the filter parameter efficiently in different conditions, which improves the adaptivity of the denoising algorithm for chaotic signals based on collaborative filtering.