Review on solving the inverse problem in EEG source analysis

Abstract

In this primer, we give a review of the inverse problem for EEG source localization. This is intended

for the researchers new in the field to get insight in the state-of-the-art techniques used to find

approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore,

a review of the performance results of the different techniques is provided to compare these

different inverse solutions. The authors also include the results of a Monte-Carlo analysis which

they performed to compare four non parametric algorithms and hence contribute to what is

presently recorded in the literature. An extensive list of references to the work of other

researchers is also provided.

This paper starts off with a mathematical description of the inverse problem and proceeds to

discuss the two main categories of methods which were developed to solve the EEG inverse

problem, mainly the non parametric and parametric methods. The main difference between the

two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling

within these categories are described including minimum norm estimates and their generalizations,

LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA

FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA,

subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and

computational intelligence algorithms for parametric methods. From a review of the performance

of these techniques as documented in the literature, one could conclude that in most cases the

LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher

resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable

biophysical and psychological constraints, as done by LAURA has given superior results. The

Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different

noise levels and different simulated source depths has shown that for single source localization,

regularized sLORETA gives the best solution in terms of both localization error and ghost sources.

Furthermore the computationally intensive solution given by SLF was not found to give any

additional benefits under such simulated conditions.