Inverse scattering for shape and conductivity

We consider the inverse problem of determining both the shape and the conductivity of a two-dimensional conducting scatterer from a knowledge of the far-field pattern of TM waves by solving the ill posed nonlinear equation. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. Satisfactory reconstructions have been achieved by the genetic algorithm. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction has been obtained. Numerical results show that multiple incident directions permit good reconstruction of shape and conductivity.