Keep it simple: a case for using classical minimum norm estimation in the analysis of EEG and MEG data.
The present study aims at finding the optimal inverse solution for the bioelectromagnetic inverse problem in the absence of reliable a priori information about the generating sources. Three approaches to tackle this problem are compared theoretically: the maximum-likelihood approach, the minimum norm approach, and the resolution optimization approach. It is shown that in all three of these frameworks, it is possible to make use of the same kind of a priori information if available, and the same solutions are obtained if the same a priori information is implemented. In particular, they all yield the minimum norm pseudoinverse (MNP) in the complete absence of such information. This indicates that the properties of the MNP, and in particular, its limitations like the inability to localize sources in depth, are not specific to this method but are fundamental limitations of the recording modalities. The minimum norm solution provides the amount of information that is actually present in the data themselves, and is therefore optimally suited to investigate the general resolution and accuracy limits of EEG and MEG measurement configurations. Furthermore, this strongly suggests that the classical minimum norm solution is a valuable method whenever no reliable a priori information about source generators is available, that is, when complex cognitive tasks are employed or when very noisy data (e.g., single-trial data) are analyzed. For that purpose, an efficient and practical implementation of this method will be suggested and illustrated with simulations using a realistic head geometry.
Hauk
Olaf
O
Cognition and Brain Sciences Unit, Medical Research Council, Cambridge, UK. olaf.hauk@mrc-cbu.cam.ac.uk
D000200:Action Potentials / Q000502:physiology; D001931:Brain Mapping; D002540:Cerebral Cortex / Q000502:physiology*; D003196:Computer Graphics; D003198:Computer Simulation; D004569:Electroencephalography / Q000706:statistics & numerical data*; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional; D016013:Likelihood Functions; D015225:Magnetoencephalography / Q000706:statistics & numerical data*; D012016:Reference Values; D012815:Signal Processing, Computer-Assisted