A Simple Regularization Scheme for Imaging Homogeneous Targets Buried Under a Rough Interface

In the framework of non-invasive diagnostics of buried structures microwave to- mography techniques are an extremely powerful tool to achieve a quantitative description of the investigated region. However, for these techniques to be successful, a suitable choice of the elec- tromagnetic modelling of the scenario, as well as reliable and accurate inversion techniques are required. Those issues become even more relevant in practical applications, wherein the nonpla- nar nature of the air-soil interface has to be properly taken into account. As a matter of fact, collected data are strongly in°uenced by the surface pro¯le, so that it is extremely di±cult to separate the contributions to the scattered data which are related to roughness from those which are concerned with the target and which are therefore of actual interest in the framework of the imaging process. In this communication we show how a simple regularization technique can be exploited to deal with this kind of problem. In particular, the proposed technique allows the simultaneous reconstruction of the buried targets and the interface roughness pro¯le. The main idea is that of considering the roughness pro¯le as a part of the unknown permittivity, i. e., as a volumetric inclusion of air in the soil. By assuming also that, as commonly experienced in applications, the unknown target is homogeneous, the overall imaging problem is then recast as the reconstruction of a piece-wise continuous function of not-connected support. Notably, as we consider the roughness pro¯le as a perturbation with respect to the planar interface case, the proposed technique does not require any complex model for the electromagnetic scenario, since the \background" is actually described by the canonical Sommerfeld-Green functions. Therefore, by taking into account the two circumstances above, the proposed inversion method is a \stan- dard" modi¯ed gradient approach as formulated for the planar layers case, in which a properly weighted penalty term is added to enforce the homogeneous and not-connected nature of the unknown function (i. e. the actual target + the air inclusion).