Equivalence of linear approaches in bioelectromagnetic inverse solutions

Several different techniques have appeared in the magnetoencephalography (MEG) literature for solving the ambiguous inverse problem. We show that if the same second order statistics are uniformly applied in each case, then the resulting solutions are the same. Additionally, for the common assumption of independent sources, then the "noise significance " measure emphasises the need to select the data and noise covariance statistics, not the specific values of source statistics. Thus such algorithms as "dynamic SPM" and "synthetic aperture magnetoencephalography " are theoretically equivalent and differ in practice by practical matters of specification or estimation of data covariances.