The inverse source problem for Maxwell's equations

The inverse source problem for Maxwell's equations is considered. We show that the problem of finding a volume current density from surface measurements does not have a unique solution, and we characterize the non-uniqueness. We also show that if further information is available the inverse source problem may have a unique solution. The method is useful for the quantitative determination of interior brain currents from surface electroencephalographic measurements. The application is to prosthesis control.