We consider the inverse problem of determining both the shape and the conductivity of a two-dimensional (2D) conducting scatterer from the knowledge of the far-field pattern of TM waves by solving the ill-posed nonlinear equation. Based on the boundary condition and measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. Satisfactory reconstructions are achieved by the genetic algorithm. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effect of Gaussian noise on the reconstruction results is investigated. The numerical results show that multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data.
International Journal of RF and Microwave Computer-Aided Engineering 14(5), pp.433-440