The Inverse Ill-Posed Problem of Magnetoencephalography

This paper continues a series of studies dealing with noninvasive preoperative methods for localizing eloquent areas of the human brain. The inverse problem of magnetoencephalography (MEG) is illposed and difficult for both analytical and numerical solutions. An analytical formula is derived for the solution of the forward problem that computes the magnetic field on the surface of the head from the known location and orientation of a current dipole in the low-frequency approximation in the spherical model. In addition, the paper considers the question of stability of solutions of the inverse problem of MEG to the effect of noise. The solution is unstable to the effect of noise on its angular component, but the deviation from the true solution is much less than the noise variance. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.