The Landweber iteration applied to inverse conductive scattering problems

The scattering of incident plane waves by a penetrable obstacle covered with a thin sheet leads to the inverse problem under consideration. We investigate the recovery of obstacles from measurements of the far-field patterns of scattered fields. The domain derivative of the operator mapping a boundary of an obstacle on the far-field pattern is presented. This result can be used to derive iterative regularization methods solving the ill-posed and nonlinear inverse problem. A suggestion of such a scheme, the Landweber iteration, is discussed in detail and some numerical results show the performance of the algorithm.