Bayesian Approach to the Illposed EEG Inverse Problem 
Thorsteinn Mar Arinbjarnarson

Abstract  Scalp recorded EEG signals are caused by neural currents in the brain. The brain currents are believed to be related to behavior and cognition. Estimating the current density from EEG recordings is the inverse EEG problem. The EEG inverse problem is highly underdetermined and some assumptions have to be made when solving it. Here assumptions will be made in the form of probability distributions describing the neural current distribution and the signal noise. Bayes theorem enables detailed analytical calculations to be made. These calculations lead to equations used to formulate iterative algorithms. Basic Gaussian distribution assumption gives a simple and robust algorithm. Automatic relevance determination (ARD) is used to from a more sparse current estimate. An original update formula is presented in the ARD algorithm which the author has not found elsewhere. Smoothing is also incorporated into the algorithms to account for localized currents.
Simulations are presented for evaluation purposes of the different methods. These tests show the different properties of the algorithms. The Gaussian algorithm converges fast and is the most robust. For sparse sources the ARD algorithm gives better estimates but for realistic forward models it usually fails. Adding spatial smoothing into the ARD iteration improves its performance and good results are obtained for realistic forward models. An attempt is made to incorporate smoothing into the Bayesian framework but the resulting algorithm does not perform better than the ARD one. Finally some real data is analyzed using the algorithms. 
Type  Master's thesis [Academic thesis] 
Year  2007 
Publisher  Informatics and Mathematical Modelling, Technical University of Denmark, DTU 
Address  Richard Petersens Plads, Building 321, DK2800 Kgs. Lyngby 
Series  IMMThesis200777 
Note  Supervised by Prof. Lars Kai Hansen, IMM, DTU. 
Electronic version(s)  [pdf] 
BibTeX data  [bibtex] 
IMM Group(s)  Intelligent Signal Processing 