Time-Varying Nonlinear Causality Detection Using Regularized Orthogonal Least Squares and Multi-Wavelets With Applications to EEG

A new transient Granger causality detection method is proposed based on a time-varying parametric modeling framework, and is applied to the real EEG signals to reveal the causal information flow during motor imagery (MI) tasks. The time-varying parametric modeling approach employs a nonlinear autoregressive with external input model, whose parameters are approximated by a set of multi-wavelet basis functions. A regularized orthogonal least squares (ROLS) algorithm is then used to produce a parsimonious or sparse regression model and estimate the associated model parameters. The time-varying Granger causality between nonstationary signals can be detected accurately by making use of both the good approximation properties of multi-wavelets and the good generalization performance of the ROLS in the presence of high-level noise. Two simulation examples are presented to demonstrate the effectiveness of the proposed method for both linear and nonlinear causal detection respectively. The proposed method is then applied to real EEG signals of MI tasks. It follows that transient causal information flow over the time course between various sensorimotor related channels can be successfully revealed during the whole reaction processes. Experimental results from these case studies confirm the applicability of the proposed scheme and show its utility for the understanding of the associated neural mechanism and the potential significance for developing MI tasks based brain-computer interface systems.