  Objective: This study proposes a new parametric TF (time frequency) CGC
(conditional Granger causality) method for high precision connectivity analysis
over time and frequency in multivariate coupling nonstationary systems, and
applies it to scalp and source EEG signals to reveal dynamic interaction
patterns in oscillatory neocortical sensorimotor networks. Methods: The Geweke
spectral measure is combined with the TVARX (time varying autoregressive with
exogenous input) modelling approach, which uses multiwavelets and ultra
regularized orthogonal least squares (UROLS) algorithm aided by APRESS
(adjustable prediction error sum of squares), to obtain high resolution time
varying CGC representations. The UROLS APRESS algorithm, which adopts both the
regularization technique and the ultra least squares criterion to measure not
only the signal data themselves but also the weak derivatives of them, is a
novel powerful method in constructing time varying models with good
generalization performance, and can accurately track smooth and fast changing
causalities. The generalized measurement based on CGC decomposition is able to
eliminate indirect influences in multivariate systems. Results: The proposed
method is validated on two simulations and then applied to multichannel motor
imagery (MI) EEG signals at scalp and source level, where the predicted
distributions are well recovered with high TF precision, and the detected
connectivity patterns of MI EEG data are physiologically and anatomically
interpretable and yield new insights into the dynamical organization of
oscillatory cortical networks. Conclusion: Experimental results confirm the
effectiveness of the proposed TF CGC method in tracking rapidly varying
causalities of EEG based oscillatory networks. Significance: The novel TF CGC
method is expected to provide important information of neural mechanisms of
perception and cognition.
