Artifact Removal from Single-Trial ERPs using Non-Gaussian Stochastic Volatility Models and Particle Filter

This paper considers improved modeling of artifactual noise for denoising of single-trial event-related potentials (ERPs) by state-space approach. Instead of the inadequate constant variance models used in existing studies, we propose to use stochastic volatility (SV) models to better describe the time-varying volatility in real ERP noise sources. We further propose a class of non-Gaussian SV models to capture the abrupt volatility changes typically present in impulsive noise, to improve artifact removal from ERPs. Two specifications are considered: (1) volatility driven by a heavy-tailed component and (2) transformation of volatility. Both result in volatility processes with heavy-tailed transition densities which can predict the impulsive noise volatility dynamics, more accurately than the Gaussian models. These SV noise models are incorporated in an autoregressive (AR) state-space ERP dynamic model. Parameter estimation is done using a Rao-Blackwellized particle filter (RBPF). Evaluation on simulated auditory brainstem responses (ABRs), corrupted by real eye-blink artifacts, shows that the non-Gaussian models can accurately detect the artifact-induced abrupt volatility spikes, and able to uncover the underlying inter-trial dynamics. Among them, the log-SV model performs the best. The results on real data demonstrate significant artifact suppression.