Asymptotic SNR of scalar and vector minimum-variance beamformers for neuromagnetic source reconstruction

To reconstruct neuromagnetic sources, the minimum-variance beamformer has been extended to incorporate the three-dimensional vector nature of the sources, and two types of extensions-the scalar- and vector-type extensions-have been proposed. This paper discusses the asymptotic signal-to-noise ratio (SNR) of the outputs of these two types of beamformers. We first show that these two types of beamformers give exactly the same output power and output SNR if the beamformer pointing direction is optimized. We then compare the output SNR of the beamformer with optimum direction to that of the conventional vector beamformer formulation where the beamformer pointing direction is not optimized. The comparison shows that the beamformer with optimum direction gives an output SNR superior to that of the conventional vector beamformer. Numerical examples validating the results of the analysis are presented.