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Functional connectivity (FC) can be represented as a network, and isfrequently used to better understand the neural underpinnings of complex taskssuch as motor imagery (MI) detection in brain-computer interfaces (BCIs).However, errors in the estimation of connectivity can affect the detectionperformances. In this work, we address the problem of denoising commonconnectivity estimates to improve the detectability of different connectivitystates. Specifically, we propose a denoising algorithm that acts on the networkgraph Laplacian, which leverages recent graph signal processing results.Further, we derive a novel formulation of the Jensen divergence for thedenoised Laplacian under different states. Numerical simulations on syntheticdata show that the denoising method improves the Jensen divergence ofconnectivity patterns corresponding to different task conditions. Furthermore,we apply the Laplacian denoising technique to brain networks estimated fromreal EEG data recorded during MI-BCI experiments. Using our novel formulationof the J-divergence, we are able to quantify the distance between the FCnetworks in the motor imagery and resting states, as well as to understand thecontribution of each Laplacian variable to the total J-divergence between twostates. Experimental results on real MI-BCI EEG data demonstrate that theLaplacian denoising improves the separation of motor imagery and resting mentalstates, and shortens the time interval required for connectivity estimation. Weconclude that the approach shows promise for the robust detection ofconnectivity states while being appealing for implementation in real-time BCIapplications.

Improving J-divergence of brain connectivity states by graph Laplacian denoising