Continuous-time non-linear non-gaussian state-space modeling of electroencephalography with sequential Monte Carlo based estimation

Abstract

Biomedical time series are non-stationary stochastic processes with hidden dynamics that can be modeled by state-space models (SSMs), and processing of which can be cast into optimal filtering problems for SSMs. The existing studies assume discrete-time linear Gaussian SSMs with estimation solved analytically by Kalman filtering for biomedical signals which are continuous, non-Gaussian and non-linear. However, general non-linear non-Gaussian models admit no closed form filtering solutions. This research investigates the general framework of continuoustime non-linear and non-Gaussian SSMs with sequential Monte Carlo (SMC) estimation for biomedical signals generally, electroencephalography (EEG) signal in particular, to solve two of its analysis problems. Firstly, this study proposes timevarying autoregressive (TVAR) SSMs with non-Gaussian state noise to capture abrupt and smooth parameter changes that are inappropriately modeled by Gaussian models, for parametric time-varying spectral estimation of event-related desynchronization (ERD). Evaluation results show superior parameter tracking performance and hence accurate ERD estimation by the proposed model. Secondly, a partially observed diffusion model is proposed for more natural modeling the continuous dynamics and irregularly spaced data in single-trial event-related potentials (ERPs) for single-trial estimation of ERPs in noise. More efficient Rao- Blackwellized particle filter (RBPF) is used. Evaluation on simulated and real auditory brainstem response (ABR) data shows significant reduction in noise with the underlying ERP dynamics clearly extracted. In addition, two non-linear non- Gaussian stochastic volatility (SV) models are proposed for better modeling of non- Gaussian dynamics of volatility in EEG noise especially of impulsive type. Application to denoising of simulated ABRs with artifacts shows well estimated volatility pattern and better elimination of impulsive noise with SNR improvement of 12.46dB by the best performing non-linear Cox-Ingersoll-Ross process.