A reliable identification of electric current dipoles using harmonic functions

We consider an identification problem for electric current dipoles in a spherically symmetric conductor from observation data of magnetic fields outside of the conductor. This problem can be expressed as an inverse source problem for three-dimensional Poisson equation. An application of this model is the analysis of magnetoencephalography. We propose a reliable numerical method for the above inverse source problem without using a priori information of the locations, moments, and number of dipoles. For two-dimensional case, an identification method of dipoles using harmonic functions has been proposed. We extend this method to three-dimensional problem, and also give error estimates for identified locations and moments. The effectiveness of our method is shown by numerical examples.