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.

Unsupervised Segmentation of Head Tissues from Multi-modal MR Images for EEG Source Localization

“…However, it is a time-consuming and laborious process [1]. A number of automatic non-invasive EEG source localization techniques [2] have been developed to overcome this problem. The accuracy of these techniques is not only dependent on the methods used to solve the underlying forward and inverse problems [3] but also on the quality and fidelity of the patient-specific head conductivity model used in the forward problem.…”

Bayesian EEG source localization using a structured sparsity prior

“…It is very classical to assume that the noise samples are independent and identically distributed according to a Gaussian distribution (Grech et al, 2008). Note that when this assumption does not hold it is possible to estimate the noise covariance matrix from measurements that do not contain the signal of interest and use it to whiten the data (Maris, 2003).…”

“…Dipole-fitting models (Sommariva and Sorrentino, 2014;da Silva and Van Rotterdam, 1998) try to estimate the amplitudes, orientations and positions of a few dipoles that explain the measured data. Unfortunately, the corresponding estimators are very sensitive to the initial guess of the number of dipoles and their initial locations (Grech et al, 2008). On the other hand, the distributed-source methods model the brain activity using a large number of dipoles with fixed positions and try to estimate their amplitudes (Grech et al, 2008) by solving an ill-posed inverse problem.…”

“…Unfortunately, the corresponding estimators are very sensitive to the initial guess of the number of dipoles and their initial locations (Grech et al, 2008). On the other hand, the distributed-source methods model the brain activity using a large number of dipoles with fixed positions and try to estimate their amplitudes (Grech et al, 2008) by solving an ill-posed inverse problem. One of the most simple ways to solve this inverse problem is to use an ℓ 2 norm regularization as the minimum norm estimator (PascualMarqui, 1999) or its variants Loreta (Pascual-Marqui et al, 1994) and sLoreta (Pascual-Marqui et al, 2002).…”

“…One of the most simple ways to solve this inverse problem is to use an ℓ 2 norm regularization as the minimum norm estimator (PascualMarqui, 1999) or its variants Loreta (Pascual-Marqui et al, 1994) and sLoreta (Pascual-Marqui et al, 2002). However, these methods usually overestimate the active area size (Grech et al, 2008).…”