An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green’s function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations. 1. Introduction Subsurface imaging is an important subject in several applicative areas, including seismic and geophysical prospecting, nondestructive, testing and medical diagnostics [1–39]. Electromagnetic techniques are widely applied to face this problem. Ground penetrating radar [40] is the basic instrumentation able to retrieve discontinuities in the lower subspace (the ground). Processing of GPR data can allow an improvement in the detection and localization capabilities of the system. In some cases, neural network-based approaches have been adopted [41]. Moreover, inverse-scattering-based techniques have been proposed, too. By using these methods, the measured values of the field scattered by the discontinuities present in the lower half space are “inverted” in order to obtain the spatial distributions of dielectric parameters (e.g., the dielectric permittivity and the electric conductivity) inside a fixed inspection domain. Approaches of this kind have been proposed, for example, for the detection of water leaking from pipes [42]. If an accurate model of the buried scatterers is available, it would be possible to retrieve information about the buried objects in terms of their dielectric parameters. The present authors developed in [43] an inverse-scattering-based method for buried object imaging under the second-order Born approximation (SOBA) [21, 44–48]. By using the SOBA, the reconstruction of buried objects has been obtained with a better accuracy with respect to linearized approximations. In particular, due to the nonlinear nature of the scattering equations, in which the electric field inside the inspected region is an unknown quantity as well as the spatial distributions of the dielectric properties of the medium, the SOBA allows to approximately retrieve the field distribution, too. However, in order to detect strong discontinuities, the exact nonlinear inverse scattering formulation must be considered. This approach has been faced in [49, 50], in which strong scatterers have been
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