On the equivalence of methods for the EEG and MEG inverse problems

Abstract

Electroencephalography (EEG) and magnetoencephalography (MEG) source analysis is a crucial component in many neuroscientific and medical applications. Numerous different approaches have been suggested to solve this ill-posed inverse problem. The underlying mathematical properties of these approaches, and their relations to other existing methods, however, are often scarcely understood. In this paper, we contribute to closing this gap. Concretely, we will investigate three of the most popular classes of EEG/MEG inverse approaches, namely dipole scanning approaches, standardized low resolution brain electromagnetic tomography (sLORETA)/exact LORETA (eLORETA) -type approaches, and beamforming approaches. We will show that dipole scanning approaches and sLORETA/eLORETA-type approaches yield equivalent localization functionals. Furthermore, we will show that, in the special case of a noisy measurement of a single source, neural activity index/array-gain and synthetic aperture magnetometry/unit-noise-gain beamformers also lead to localization functionals which are equivalent to those arising from dipole scanning. Finally, we will demonstrate how these new insights close existing gaps in the understanding of sLORETA, eLORETA, and beamforming methods, by reducing the questions to the dipole scanning case, where they can be more easily answered.