The effect of artifact rejection by signal-space projection on source localization accuracy in MEG measurements

The consequences of artifact suppression by means of signal-space projection on dipole localization accuracy for magnetoencephalography measurements are studied. Approximate analytical formulas, equivalent to the Cramer-Rao bound, are presented and verified by Monte Carlo simulations which relate the increase of localization error for individual coordinates to the similarity of the artifact field and respective (contravariant) quadrupole fields obtained by differentiating the dipole field with respect to its origin. The expressions simplify significantly for dipoles placed below the center of the measuring system giving rise to highly symmetric field patterns. Formulas are presented both for single- and for multiple-artifact rejection. As illustrative examples artifact fields are constructed which (a) lead to highly decreasing signal-to-noise ratio and goodness-of-fit (GOF), while the localization error is unaffected for all coordinates and (b) lead to an increase of localization error while the SNR and the GOF stays constant. Finally, the rich structure of localization error increase is demonstrated for a class of artifact fields originating from artifact current dipoles.