Smoothing of spatial filter by graph Fourier transform for EEG signals

Spatial filtering is useful for extracting features from multichannel EEG signals. In order to enhance robustness of the spatial filter against low SNR and small samples, we propose a smoothing method for the spatial filter using spectral graph theory. This method is based on an assumption that the electrodes installed in nearby locations observe the electrical activities of the same source. Therefore the spatial filter's coefficients corresponding to the nearby electrodes are supposed to be taken similar values, that is, the coefficients should be spatially smooth. To introduce the smoothness, we define a graph whose edge weights represent the physical distances between the electrodes. The spatial filter spatially smoothed is found out in the subspace that is spanned by the smooth basis of the graph Fourier transform. We evaluate the method with artificial signals and a dataset of motor imagery brain computer interface. The smoothness of the spatial filter given by the method provides robustness of the spatial filter in the condition that the small amount of the samples is available.