1D Inverse Scattering with Backing Reflecting Plane

1D inverse profiling aims to reconstruct the dielectric profile of one-dimensional scatterers and belongs to the class of inverse scattering problems. The solution of such problems, even if addressed in a linear framework, is challenging because of their ill-posedness. Since an inhomogeneous host medium enriches the scenario because of additional scattering, we investigated the impact of a reflecting plane in a 1D linear inverse profiling problem with multi-frequency data. We analyze the mathematical features of the scattering operator by means of its singular value decomposition (SVD). The regularized inversion scheme introduces a band-pass filtering with twice as much bandwidth as in the homogeneous scenario and allows for the reconstruction of the profile's mean value. Consequently, the reflecting plane allows for the stable reconstruction of a broader class of dielectric profiles.