Multi-core beamformers: derivation, limitations and improvements

Minimum variance beamformers are popular tools used in EEG and MEG for analysis of brain activity. In recent years new multi-source beamformer methods were developed, including the Dual-Core Beamformer (DCBF) and its enhanced version (eDCBF). Both techniques should allow modeling of correlated brain activity under a wide range of conditions. However, the mathematical justification given is based on single-source results and computer simulations, which do not provide an insight into the assumptions involved and the limits of their applicability. Current work addresses this problem. Analytical expressions relating actual source parameters to those obtained with the DCBF and eDCBF are derived, and rigorous conclusions regarding the accuracy of the DCBF/eDCBF reconstructions are made. In particular, it is shown that DCBF accurately identifies source coordinates, but amplitudes and orientations are only correct for high SNRs and fully correlated sources. In contrast, eDCBF source localization is inaccurate, but if the source positions are found precisely, eDCBF allows perfect reconstruction for arbitrary SNRs. If the source positions are approximate, the reconstruction errors are generally larger for higher SNR values. The eDCBF results can be improved by using global unbiased localizer functions and an alternative way of estimating source orientations.