In this primer, we give a review of the inverse problem in EEG source localization. It is intended for the researcher who is new in the field to get insight in the state-of-the-art techniques used to get approximate solutions. It also provides an extensive list of references to the work of other researchers. The primer starts with a mathematical formulation of the problem. Then in Section 3 we proceed to discuss the two main categories of inverse methods: non parametric methods and parametric methods. For the first category we discuss minimum norm estimates and their generalizations, the Backus-Gilbert method, Weighted Resolution Optimization, LAURA, shrinking and multiresolution methods. For the second category, we discuss the non-linear least-squares problem, beamforming approaches, the Multiple-signal Classification Algorithm (MUSIC), the Brain Electric Source Analysis (BESA), subspace techniques, simulated annealing and finite elements, and computational intelligence algorithms, in particular neural networks and genetic algorithms. In Section 4 we then give an overview of source localization errors and a review of the performance analysis of the techniques discussed in the previous section. This is then followed by a discussion and conclusion which are given in Section 5.
