Two methods for solving an inverse conductive scattering problem

The inverse conductive scattering problem we are concerned with is to determine the shape of an obstacle which is covered by an infinitely thin layer or high conductivity by measurements of the far-field patterns of scattered waves. We derive two methods proposed by Kirsch, Kress and Monk (1988) and Colton and Monk (1989) respectively on numerically solving this improperly posed problem. In particular the effects of such boundary conditions are illustrated in some examples.