A Comparison of Linear Inverse Scattering Models for Contactless GPR Imaging

Ground-penetrating radars operating at a stand-off distance from the probed domain are attractive diagnostic tools in several contexts. Despite notable advantages offered in terms of noninvasiveness and flexibility, the usage of stand-off configurations makes the imaging process more difficult. Indeed, an accurate reconstruction of the subsurface/hidden scene requires accounting for the presence of the air-soil interface into the scattering model. This article deals with a comparison of three different linear models for describing the scattering phenomenon under a stand-off configuration, where the presence of the layered medium is explicitly accounted for in the scattering model. The first model is rigorous and based on the spectral domain representation of the incident field and Green's function for the half-space scenario. The second model exploits a ray representation of the wave propagation from the radar to the target and vice versa by accounting for the refraction phenomenon at the interface. The third model is an approximated one, where the layered nature of the scenario is taken into account by means of an equivalent wavenumber, which allows a straightforward evaluation of the incident field and Green's function. The resolution performance of each inversion approach is assessed by means of a numerical analysis. Moreover, data referred to an experiment carried out in controlled conditions are processed and reconstructions are provided to support the comparative analysis among the three imaging approaches.