GPR prospecting in a layered medium via microwave tomography

The tomographic approach appears to be a promising way to elaborate Ground Penetrating Radar (GPR) data in order to achieve quantitative information on the tested regions. In this paper, we apply a linearized tomographic approach to the reconstruction of dielectric objects embedded in a layered medium. The problem is tackled with reference to a two-dimensional geometry and scalar case when data are collected over a linear domain with finite extent. In particular, in order to increase the amount of independent available data, a multi-frequency/multi-view/ multi-static measurement configuration is considered. With reference to stepped-frequency radar, this means that for each working frequency and for each position of the transmitting antenna (moved along a linear domain), the electric field scattered by the buried targets is measured in several locations along the same linear domain. The proposed inversion approach is based on the Born approximation and a regularized solution is introduced by means of the Singular Value Decomposition (SVD). The problem of determining the optimal measurement configuration (in terms of number of frequencies and number of transmitting and receiving antennas) is also tackled by a numerical analysis relying on the Singular Value Decomposition (SVD). Numerical examples are provided to assess the effectiveness and robustness of the proposed approach against noise on data.