A numerical method to solve the inverse medium problem: an application to the Ipswich data

We consider the propagation of electromagnetic waves in an inhomogeneous medium. The inhomogeneity is contained in a vertical cylinder with a compact base. When an incident wave meets the inhomogeneity, a scattered wave is generated. We consider the problem of the reconstruction of the inhomogeneous refractive index from some knowledge of the scattered waves generated by the interaction of the inhomogeneity with several known incident waves. We give a mathematical formulation of the problem, a numerical method to solve it, and some numerical results obtained using the numerical method proposed on the Ipswich data. The Ipswich data are experimental data. The inverse-scattering problem considered above is of great theoretical and practical interest. It is an ill-posed problem.