On an electromagnetic inverse source problem for the excitation of a spherical medium

Important applications in medical imaging, like for example electroencephalography (EEG), frequently utilize a homogeneous dielectric sphere excited by an interior electromagnetic point-dipole as an appropriate relevant simplified model. In this work, we investigate an electromagnetic inverse source problem, where a primary magnetic dipole source radiating inside a homogeneous sphere is determined from a certain set of field measurements on the sphere's surface. More precisely, the location and strength of the interior dipole are determined by a simple and analytic methodology which relies on the information from specific moments, obtained by integrating the product of the total tangential electric field on the spherical interface with the vector spherical harmonic functions.