sLORETA is equivalent to single dipole scanning

TL;DR

This paper demonstrates that various source reconstruction methods, including sLORETA and beamformers, are mathematically equivalent to single dipole scanning under certain conditions, unifying different approaches in neuroimaging.

Contribution

It reveals the exact equivalence of sLORETA, eLORETA, and certain beamformers to single dipole scanning, providing a unified theoretical framework.

Findings

sLORETA and eLORETA are equivalent to single dipole scan.

NAI/AG and SAM/UNG beamformers are equivalent to dipole scanning in specific scenarios.

Under ideal conditions, NAI and SAM beamformers are equivalent.

Abstract

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.