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.

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Cross-frequency coupling (CFC) is thought to represent a basic mechanism of functional integration of neural networks across distant brain regions. In this study, we analyzed CFC profiles from resting state Magnetoencephalographic (MEG) recordings obtained from 30 mild traumatic brain injury (mTBI) patients and 50 controls. We used mutual information (MI) to quantify the phase-to-amplitude coupling (PAC) of activity among the recording sensors in six nonoverlapping frequency bands. After forming the CFC-based functional connectivity graphs, we employed a tensor representation and tensor subspace analysis to identify the optimal set of features for subject classification as mTBI or control. Our results showed that controls formed a dense network of stronger local and global connections indicating higher functional integration compared to mTBI patients.Furthermore, mTBI patients could be separated from controls with more than 90% classification accuracy. These findings indicate that analysis of brain networks computed from resting-state MEG with PAC and tensorial representation of connectivity profiles may provide a valuable biomarker for the diagnosis of mTBI.

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