sLORETA is equivalent to single dipole scanning

In this paper, we show that each member of a family of reconstruction approaches, which includes the classical sLORETA approach and the eLORETA approach, is exactly equivalent to a single dipole scan in some inner product norm. Additionally, we investigate NAI/AG and SAM/UNG beamformers and show that, in scenarios with a single active source with additive uncorrelated noise, they are also equivalent to some form of dipole scanning. As a particular consequence, this shows that, under ideal conditions in a noisy single source case, NAI and SAM (resp. AG and UNG) beamformers are equivalent. Finally, we also discuss how to generalize scalar beamformers to vector beamformers.