Nonlinear noise reduction using reference data

Abstract

We introduce a method to clean uncorrelated deterministic and stochastic noise components from time series. It combines recently developed techniques for nonlinear projection with properties of the wavelet transform to extract noise in state space. The method requires that time series are generated by a dynamical system which is at least approximately deterministic and that they are recorded together with a reference signal. Its efficiency was tested on both simulated signals and measured magnetic fields of the heart. Convincing results are obtained even at low signal-to-noise ratios.