### For REFEREES

 Volume 8, Number 3, 2018, Pages 915-927 Inverse problems in magneto-electroscanning (in encephalography, for magnetic microscopes, etc.) Alexandre Sergeevich Demidov Keywords:Inverse problems, integral equations, pseudo-differential operators, magneto-electroscanning Abstract: Contrary to the prevailing opinion about the incorrectness of the inverse MEEG-problem, we prove its unique solvability in the framework of the system of Maxwell''s equations [3]. The solution of this problem is the distribution of ${\bf y} \mapsto {\bf q}({\bf y})$ current dipoles of brain neurons that occupies the region $Y \subset \mathbb{R}^3$. It is uniquely determined by the non-invasive measurements of the electric and magnetic fields induced by the current dipoles of neurons on the patient""s head. The solution can be represented in the form ${\bf q}={\bf q}_0+{\bf p}_0\delta\Big|_{\partial Y}$, where ${\bf q}_0$ is the usual function defined in $Y,$ and ${\bf p}_0\delta\Big|_{\partial Y}$ is a $\delta$-function on the boundary of the domain $Y$ with a certain density ${\bf p}_0$. It is essential that ${\bf p}_0$ and ${\bf q}_0$ are interrelated. This ensures the correctness of the inverse MEEG-problem. However, the components of the required 3-dimensional distribution ${\bf q}$ must turn out to be linearly dependent if only the magnetic field ${\bf B}$ is taken into account. This question is considered in detail in a flat model of the situation. PDF      Download reader