An efficient method for the solution of the inverse scattering problem for penetrable obstacles

We consider a two-dimensional scattering problem for inhomogeneous media. This problem arises from the study of time-harmonic electromagnetic scattering problems for Transverse Magnetic (TM) waves. In the direct scattering problem we have to compute the scattered wave from the knowledge of the incident wave and of the inhomogeneity. In the inverse scattering problem we have to reconstruct the refractive index of the inhomogeneity from some knowledge of the scattered waves generated by the inhomogeneity itself with known incident waves.