Assessment of a non-Hilbertian inverse scattering approach for electromagnetic tomography in subsurface environments

In this paper, a technique for the electromagnetic tomography of buried objects is proposed. More precisely, in the present approach a finite-element (FE) formulation of the electromagnetic problem is coupled with an inversion procedure performed in non-Hilbertian variable-exponent Lebesgue spaces to provide an image of the distribution of complex dielectric permittivity in the inspected subsurface environment. A test concerning a void-filled cylindrical target imaged by a set of waveguide antennas in a two-layer configuration has been performed to validate the method.