Denoising of discrete-time chaotic signals using echo state networks

Noise reduction is a relevant topic in the application of chaotic signals in communication systems, in modeling biomedical signals or in time series forecasting. In this paper an echo state network (ESN) is employed to denoise a discrete-time chaotic signal corrupted by additive white Gaussian noise. The choice of applying ESNs in this context is motivated by their successful exploitation for the separation and prediction of continuous-time chaotic signals. Our results show that the processing gain of the ESN is higher than the one obtained using a Wiener filter for chaotic signals generated by a skew-tent map. Since the power spectral density of the orbits in this map is well known, it was possible to analyze how the processing gain of the ESN in the denoising process varies according to the spectral characteristics of the chaotic signals.