Improving the Nulling Beamformer Using Subspace Suppression

Abstract

Magnetoencephalography (MEG) captures the magnetic fields generated by neuronal current sources with sensors outside the head. In MEG analysis these current sources are estimated from the measured data to identify the locations and time courses of neural activity. Since there is no unique solution to this so-called inverse problem, multiple source estimation techniques have been developed. The nulling beamformer (NB), a modified form of the linearly constrained minimum variance (LCMV) beamformer, is specifically used in the process of inferring interregional interactions and is designed to eliminate shared signal contributions, or cross-talk, between regions of interest (ROIs) that would otherwise interfere with the connectivity analyses. The nulling beamformer applies the truncated singular value decomposition (TSVD) to remove small signal contributions from a ROI to the sensor signals. However, ROIs with strong crosstalk will have high separating power in the weaker components, which may be removed by the TSVD operation. To address this issue we propose a new method, the nulling beamformer with subspace suppression (NBSS). This method, controlled by a tuning parameter, reweights the singular values of the gain matrix mapping from source to sensor space such that components with high overlap are reduced. By doing so, we are able to measure signals between nearby source locations with limited cross-talk interference, allowing for reliable cortical connectivity analysis between them. In two simulations, we demonstrated that NBSS reduces cross-talk while retaining ROIs' signal power, and has higher separating power than both the minimum norm estimate (MNE) and the nulling beamformer without subspace suppression. We also showed that NBSS successfully localized the auditory M100 event-related field in primary auditory cortex, measured from a subject undergoing an auditory localizer task, and suppressed cross-talk in a nearby region in the superior temporal sulcus.