Optimization of detectability and resolution
                  in an electrical tomography problem

                           by Elena Cherkaeva

               JWB 335, 3:20pm  Monday, October 23, 1995

                                Abstract

   The talk deals with the problem of maximizing the response from an
   unknown inclusion when arbitrary currents can be injected on the
   boundary of the conducting body and the corresponding potentials are
   measured. The optimal currents, i.e. the currents which maximize the
   response difference on the boundary for the real and an assumed
   background media, are eigenfunctions of an operator mapping the
   injected currents to the measured voltage difference. These currents
   maximize the energy of the scattering current in the region of the
   inclusion over a set of possible boundary currents, similarly to the
   eigenfunctions of the Neumann to Dirichlet map which maximize the
   energy dissipated in the body. When the energy of current injection
   is measured, the detectability is equal to the difference of energies
   needed to inject currents in the model body without inclusion and in
   the real medium. The bounds of detectability are established which
   are independent of the shape of the domain and have a simple
   analytical form.