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Objective: This study proposes a new parametric TF (time frequency) CGC(conditional Granger causality) method for high precision connectivity analysisover time and frequency in multivariate coupling nonstationary systems, andapplies it to scalp and source EEG signals to reveal dynamic interactionpatterns in oscillatory neocortical sensorimotor networks. Methods: The Gewekespectral measure is combined with the TVARX (time varying autoregressive withexogenous input) modelling approach, which uses multiwavelets and ultraregularized orthogonal least squares (UROLS) algorithm aided by APRESS(adjustable prediction error sum of squares), to obtain high resolution timevarying CGC representations. The UROLS APRESS algorithm, which adopts both theregularization technique and the ultra least squares criterion to measure notonly the signal data themselves but also the weak derivatives of them, is anovel powerful method in constructing time varying models with goodgeneralization performance, and can accurately track smooth and fast changingcausalities. The generalized measurement based on CGC decomposition is able toeliminate indirect influences in multivariate systems. Results: The proposedmethod is validated on two simulations and then applied to multichannel motorimagery (MI) EEG signals at scalp and source level, where the predicteddistributions are well recovered with high TF precision, and the detectedconnectivity patterns of MI EEG data are physiologically and anatomicallyinterpretable and yield new insights into the dynamical organization ofoscillatory cortical networks. Conclusion: Experimental results confirm theeffectiveness of the proposed TF CGC method in tracking rapidly varyingcausalities of EEG based oscillatory networks. Significance: The novel TF CGCmethod is expected to provide important information of neural mechanisms ofperception and cognition.

A Parametric Time Frequency-Conditional Granger Causality Method Using  Ultra-regularized Orthogonal Least Squares and Multiwavelets for Dynamic  Connectivity Analysis in EEGs