Signal-noise separation using unsupervised reservoir computing

Removing noise from a signal without knowing the characteristics of the noise is a challenging task. This paper introduces a signal-noise separation method based on time-series prediction. We use Reservoir Computing (RC) to extract the maximum portion of "predictable information" from a given signal. Reproducing the deterministic component of the signal using RC, we estimate the noise distribution from the difference between the original signal and the reconstructed one. The method is based on a machine-learning approach and requires no prior knowledge of either the deterministic signal or the noise distribution. It provides a way to identify additivity/multiplicativity of noise and to estimate the signal-to-noise ratio (SNR) indirectly. The method works successfully for combinations of various signals and noise, including the chaotic signal and the highly oscillating sinusoidal signal, which are corrupted by non-Gaussian additive/multiplicative noise. The separation performances are robust and notably outstanding for signals with strong noise, even for those with negative SNR.