Localization of the Interfaces of a Slab Hidden Behind a Wall

In this paper, a 1-D inverse-scattering problem laying within the framework of through-wall imaging is addressed. In particular, the problem of localizing the interfaces of a slab hidden behind an obstacle, another slab whose electromagnetic features and thickness are known, is considered. To this end, an approximate linear mathematical relationship between the scattered field and the unknown slab-interface positions is stated. Such an approximate relationship arises from neglecting the multiple-reflections between the two unknown slab´s interfaces and between the slab and the obstacle. The unknown locations of the slab´s interfaces are represented as the support of Dirac-delta functions, and the problem is cast as the inversion of a linear integral operator whose inversion is achieved by means of the Truncated-Singular-Value-Decomposition (TSVD) inversion scheme. The effect of the parameters of the obstacle on the inversion algorithm and the performances achievable by the solution approach are assessed by exploiting synthetic data. Furthermore, a comparison with the reconstructions obtained under the Born approximation and with the time-backscattered field is achieved. Finally, results obtained by employing experimental data collected owing to a stepped-frequency ground-penetrating radar system are also presented.