On Linearly Constrained Minimum Variance Beamforming

Beamforming is a widely used technique for source localization in signal processing and neuroimaging. A number of vector-beamformers have been introduced to localize neuronal activity by using

magnetoencephalography (MEG) data in the literature. However, the existing theoretical analyses

on these beamformers have been limited to simple cases, where no more than two sources are allowed in the associated model and the theoretical sensor covariance

is also assumed known. The information about the effects of the MEG spatial and temporal dimensions on the consistency of vector-beamforming is incomplete.

In the present study, we consider a class of vector-beamformers defined by thresholding the sensor covariance matrix, which include the standard vector-beamformer as a special case.

A general asymptotic theory is developed for

these vector-beamformers, which shows the extent of effects to which the MEG spatial and temporal dimensions on estimating the neuronal activity index. The performances of the proposed beamformers are assessed by simulation studies. Superior performances of the proposed beamformers are obtained

when the signal-to-noise ratio is low.

We apply the proposed procedure to real MEG datasets derived from five sessions of a human face-perception experiment, finding several highly active areas in the brain. A good agreement between these findings and the known neurophysiology of the MEG response to human face perception is shown.