Image reconstruction from total electric field data with no information on incident field

We present an inverse scattering method using only total electric field data on an observation surface with no knowledge of incident fields. An initial-boundary value problem is set up whose solution coincides with that of the original scattering problem in the interior region bounded by the observation surface if and only if a medium inside the observation surface is the same as that of the original one. A cost functional consisting the stored energy of the misfit field between the original problem and the boundary value problem with an estimated object is introduced to solve the inverse problem. Preliminary numerical examples are provided to assess the proposed inversion approach.