Expectation–maximization algorithm with a nonlinear kalman smoother for MEG/EEG connectivity estimation

Abstract

Current techniques to determine functional or effective connectivity from magnetoencephalography (MEG) and electroencephalography (EEG) signals typically involve two sequential steps: 1) estimation of the source current distribution from the sensor data, for example, by minimum-norm estimation or beamforming, and 2) fitting a multivariate autoregressive (MVAR) model to estimate the AR coefficients, which reflect the interaction between the sources. Here, we introduce a combination of the expectation–maximization (EM) algorithm and a nonlinear Kalman smoother to perform joint estimation of both source and connectivity (linear and nonlinear) parameters from MEG/EEG signals. Based on simulations, we show that the proposed approach estimates both the source signals and AR coefficients in linear models significantly better than the traditional two-step approach when the signal-to-noise ratio (SNR) is low (≤1) and gives comparable results at higher SNRs (>1). Additionally, we show that nonlinear interaction parameters can be reliably estimated from MEG/EEG signals at low SNRs using the EM algorithm with sigma-point Kalman smoother.