Sensor space time-varying information flow analysis of multiclass motor imagery through Kalman Smoother and EM algorithm

Inter-channel time-varying (TV) relationships of scalp neural recordings offer deep understanding of the brain sensory and cognitive functions. This paper develops a state space-based TV multivariate autoregressive (MVAR) model for estimating TV-information flow (IF) recruited by different motor imagery (MI) movements. TV model coefficients are computed through Kalman filter (KF) by incorporating Kalman smoothing approach and expectation-maximization algorithm for model parameter estimation, KS-EM. Volume conduction (VC) problem is also addressed by considering full noise covariate in observation equation. An automated model initialization is also implemented to deliver optimal estimates. TV-partial directed coherence derived from the proposed model is applied for IF analysis. The performance of KS-EM is assessed and compared with dual extended KF and overlapping sliding window-based MVAR models using simulated data. Finally, TV-IF during four different MI movements is studied. Results show the superiority of KS-EM for tracking the rapid signal parameter changes and eliminating the VC effect in the sensor space EEG. Differences in contralateral/ipsilateral TV-IF around alpha and lower beta bands during each MI task reveal the high potential of this feature for BCI applications.