Solution of the Biomagnetic Inverse Problem
Area: Electrical Engeneering
In magnetoencephalography (MEG) a weak magnetic field induced by the electrical activity of the brain is recorded at little distance outside the head. The mathematical model to localize the electrical activity from the measurements is given by an inverse problem.
In 1853 Helmholtz showed that there is no unique reconstruction of a current distribution for a given magnetic field. Therefore, several reconstruction approaches exist. Here, the minimum p-norm approach based on calculating the magnetic field outside the head from a superposition of current dipoles inside inside the head is used. The current distribution matching the given magnetic field best in the minimum p-norm minimization problem is tackled with a gradient-based optimization technique. The required gradient of length 1098 is computed by the reverse mode of automatic differentiation.