An inverse scattering problem from an impedance obstacle

In this paper we consider an inverse scattering problem from an obstacle with impedance boundary condition. Our aim is to recover the unknown scatterer from the far field pattern iteratively assuming the impedance function. Our method, while remaining in the framework of Newton’s method, based on a system of two nonlinear integral equations which is equivalent to the original inverse problem, avoids the need of calculating a direct problem at each iteration. Because of the ill-posedness of this problem, regularization method for example, Tikhonov regularization, is incorporated in our solution scheme. Several numerical examples with only one incident wave are given at the end of the paper to show the feasibility of our method.