The article presents an imaging approach for ground penetrating radar prospecting over a heterogeneous background soil characterized by a dielectric permittivity variation along depth. The proposed approach is based on a linear model of the electromagnetic scattering phenomenon, where the soil inhomogeneity in the reference scenario is accounted for by introducing an equivalent permittivity function. Such a function notably simplifies the computation of the kernel of the relevant linear integral equation to be inverted. Then, the data inversion is carried out in a regularized way by resorting to the truncated singular value decomposition scheme. A procedure for estimating the equivalent permittivity function, typically unknown in practical situations, is also proposed. Reconstruction results achieved from full-wave simulated data and real data collected in a controlled test site are provided to demonstrate the effectiveness and the reliability of the proposed imaging approach.