Unsupervised reservoir computing for multivariate denoising of severely contaminated signals

Abstract

The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach must consider not only the multivariate dependencies of the desired signal but also the multivariate dependencies of the interfering noise. In our previous research, we introduced a method using machine learning to extract the maximum portion of “predictable information” from univariate signal. We extend this approach to multivariate signals with a key innovation: an interference calibration matrix that incorporates directional noise intensities back into signal reconstruction. The method applies PCA to the noise covariance matrix to identify noise variance in each principal direction, then assigns directional weights based on signal-tonoise ratios to improve reconstruction ccuracy. The method works successfully for various multivariate signals, including chaotic signals and highly oscillating sinusoidal ignals which are corrupted by spatially correlated intensive Gaussian/non-Gaussian noise. It consistently outperforms other existing multivariate denoising methods by 3-6 dB across a wide range of scenarios including real-world data.