Inverse scattering approach by using cost functional consisting the approximated stored energy with no information on incident field

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. Based on this initial- boundary value problem, we present an inverse scattering method by using cost functional consisting the approximated stored energy with no information on incident field. A cost functional consisting of the approximated 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.