Inversion of ground penetrating radar data in nonconstant-exponent Lebesgue spaces

Ground Penetrating Radar (GPR) is a non-invasive imaging technique widely adopted in subsurface prospection, e.g., for soil mapping, demining, utility detection, road pavement monitoring, etc. The output of GPR systems is usually provided as a B-scan, i.e., a two-dimensional plot of the received electromagnetic signal versus time. However, such a representation is usually difficult to interpret and requires skilled users. A significant enhancement could be obtained by applying inverse-scattering techniques, which are in principle able to directly provide an image of the dielectric properties of the inspected region. In this contribution, a novel inversion procedure is presented. It is based on an outer-inner inexactNewton scheme, in which the linear problem obtained at each Newton step is solved by using a Landweber-like procedure performing a regularization in the framework of the variable-exponent Lebesgue spaces . The exponent function is adaptively built during iterations by exploiting the currently retrieved solution. In particular, low values of are assigned to the background, in order to enhance the sparsity of the solution in this region, whereas values close to 2 are used inside targets. The developed approach allows obtaining better results than the corresponding Hilbert-space method. Moreover, it allows avoiding the manual selection of the exponent parameter, which is the main drawback of fixed-exponent Lebesguespace techniques.