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Inverse MEG and EEG

  Inverse Problems of MEG and EEG

MEG (magnetoencephalography) and EEG (electroencephalography) are techniques for the measurement of the magnetic and electric fields of the brain. These fields are caused by current distributions and electric charges inside the brain. The task of the inverse problems of MEG and EEG is to compute the currents inside the brain out of MEG and EEG data. This inverse problem is, like many inverse problems in practice, ill-posed. This is, in particular the case because the solution is not unique and not stable, i.e. small errors in the measurements can cause completely different solutions.

In cooperation with AS Fokas at the University of Cambridge and Olaf Hauk at the MRC Cognition and Brain Sciences Unit in Cambridge, UK, the Geomathematics Group in Siegen is investigating this inverse problem with respect to theoretical and numerical aspects. For instance, a spline method originating from Willi Freeden was successfully adapted to the inverse MEG problem.

 

References:

  • A.S. Fokas, O. Hauk, V. Michel: Electro-magneto-encephalography for the three-shell model: numerical implementation via splines for distributed current in spherical geometry, Inverse Problems, 28 (2012), 035009 (28pp).
  • V. Michel, S. Orzlowski: On the Null Space of a Class of Fredholm Integral Equations of the First Kind, accepted for publication in: Journal of Inverse and Ill-Posed Problems, 2015, published online.