Reduced-rank beamforming for brain source localization in presence of high background activity

We consider the problem of electroencephalography (EEG) source localization using beamforming techniques. Specifically, we propose a reduced-rank extension of the multi-source activity index (MAI), which itself is an extension of the classical neural activity index to the multi-source case. It is well known that source localization through MAI does not work well under the presence of high background activity, mainly due to the ill-conditioning of the measurement and noise covariance matrices. For this reason, we propose an alternative index based on the structure of the generalized sidelobe canceler (GSC) in which the cross-covariance matrix of the brain and noise-plus-interfering sources is approximated through its highest cross-spectral metrics. Under this condition, the cross-covariance only takes into account the eigencomponents with higher affinity to the main brain sources and leaves out other background activity. Our realistic simulations show that our proposed method achieves a more consistent source localization than the full-rank MAI, specifically for the case of three brain sources embedded in high background activity that originates at the brain cortex and thalamus. We also discuss the limitations of our method, which are related to the selection of the optimum rank and its computational cost.