Nonlinear inverse-scattering in variable-exponent spaces for multifrequency subsurface imaging

In this paper, a subsurface imaging configuration is considered, with the goal of retrieving the quantitative dielectric properties of buried targets from scattered electric field measurements performed by a set of antennas above the soil. The acquired scattered-field data are processed by a nonlinear inverse-scattering approach in variable-exponent Lebesgue spaces able to jointly exploit multifrequency data, which is extended here for the first time to subsurface imaging problems. Numerical simulations are presented as a preliminary assessment of the proposed inverse-scattering technique, where a multistatic ground penetrating radar configuration is adopted.