The Inverse EEG and MEG Problems : The Adjoint State Approach I: The Continuous Case
Abstract
In this report, we study the problem of the three-dimensional reconstruction of the electrical activity of the brain from electroencephalography (EEG) and magnetoencephalography (MEG). We use a variational approach based upon three main methods and ideas. The first one is the optimal control of systems governed by elliptic partial differential equations, the second is the regularization of the solutions while preserving the discontinuities (the edges), and the third one is the use of geometric information obtained from magnetic resonance images (MRI) to constrain the solutions in an anatomically «reasonable» way.
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