  Functional connectivity (FC) can be represented as a network, and is
frequently used to better understand the neural underpinnings of complex tasks
such as motor imagery (MI) detection in brain-computer interfaces (BCIs).
However, errors in the estimation of connectivity can affect the detection
performances. In this work, we address the problem of denoising common
connectivity estimates to improve the detectability of different connectivity
states. Specifically, we propose a denoising algorithm that acts on the network
graph Laplacian, which leverages recent graph signal processing results.
Further, we derive a novel formulation of the Jensen divergence for the
denoised Laplacian under different states. Numerical simulations on synthetic
data show that the denoising method improves the Jensen divergence of
connectivity patterns corresponding to different task conditions. Furthermore,
we apply the Laplacian denoising technique to brain networks estimated from
real EEG data recorded during MI-BCI experiments. Using our novel formulation
of the J-divergence, we are able to quantify the distance between the FC
networks in the motor imagery and resting states, as well as to understand the
contribution of each Laplacian variable to the total J-divergence between two
states. Experimental results on real MI-BCI EEG data demonstrate that the
Laplacian denoising improves the separation of motor imagery and resting mental
states, and shortens the time interval required for connectivity estimation. We
conclude that the approach shows promise for the robust detection of
connectivity states while being appealing for implementation in real-time BCI
applications.
