A method for MEG data that obtains linearly-constrained minimum-variance beamformer solution by minimum-norm least-squares method

Abstract

A method to obtain the linearly-constrained minimum-variance (LCMV) beamformer solution simply by applying the minimum-norm least-squares (MNLS) method to the recorded brain magnetic fields is theoretically shown. First, apply the prewhitening process to the recorded data using the data variance-covariance matrix. Then, apply the MNLS method to its outcome. The obtained solution is mathematically proved to be equivalent to the one obtained by the original LCMV beamformer. This method works only when the number of independent neural currents (equivalent to double of the number of specified neural current locations if a spherical head model is used) in the brain to be calculated is not more than the number of magnetic sensors. This is because linear independence of the neural currents is one of prerequisites for obtaining the LCMV beamformer weight matrices. When it is more, the solution currents at different locations are not linearly independent, meaning that the obtained neural currents are mathematically, rather than physiologically, determined by the beamformer weight matrices or the MNLS pseudoinverse matrix, which should be avoided for further analyses on the obtained neural currents. © Springer-Verlag 2010.