High-order inversion formulas for 3D buried dielectric objects

Abstract

In this work, we propose an efficient inversion method to reconstruct 3D dielectric objects buried in a lossy earth using the high-order extended Born (ExBorn) approximations. We have shown that the zeroth-order solution of the method is completely equivalent to the Born approximation, which corresponds to a linear inverse scattering. Based on the high-order ExBorn approximations for forward scattering problem, high-order solutions of the object function for inverse scattering problems are obtained, which have closed-form relations to the linear inverse-scattering solution. Because such relations can be fast evaluated using the fast Fourier transform, the high-order solutions have similar simplicity to the Born approximation. When the contrast of buried object is large, the high-order solutions are much more accurate due to the approximate consideration of multiple-scattering effect within the object. Therefore, good resolution images can be obtained for large-contrast objects using the new method by only solving a linear inverse-scattering problem. In the linear inversion, a modified Tikhonov regularization has been adopted, which can provide better reconstruction results than the conventional Tikhonov regularization. Numerical experiments have shown the validity and efficiency of the proposed method.