High-order inversion formulas for low-frequency imaging of 2D buried targets

In this work, new closed-form formulations are derived for the inverse scattering of 2D large-contrast dielectric objects, buried in a lossy earth, using the idea of back-conditioner and lumped-mass approximation. These formulations are also valid to the case of free space. It has been demonstrated that the zeroth-order form of the new approximation is just the well-known Born approximation, and the first-order form is completely equivalent to the quasi-linear approximation. Hence, high-order approximations are proposed in this work for the imaging of buried objects in lossy earth. Reconstruction examples show the validity and efficiency of these formulations.