Unsupervised Reservoir Computing for Multivariate Denoising of Severely Contaminated Signals

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 the key idea being to properly incorporate the interdependencies of the noise back into the interdependent reconstruction of the signal. The method works successfully for various multivariate signals, including chaotic signals and highly oscillating sinusoidal signals which are corrupted by spatially correlated intensive noise. It consistently outperforms other existing multivariate denoising methods across a wide range of scenarios.