Low-frequency detection of two-dimensional buried objects using high-order extended Born approximations

Linear inverse scattering method based on the Born approximation has found wide applications in the on-site detection of buried objects, such as in diffraction tomography. However, the Born approximation becomes invalid when the contrast of targets is high, in which the multiple-scattering effect within the target is more important. To avoid solving the nonlinear inverse scattering problem for large-contrast objects, quasi-linear and modified quasi-linear approximations are proposed based on the extended Born approximation. In this paper, new formulations are derived for the inversion of large-contrast dielectric objects buried in a lossy earth using the idea of backconditioner and lumped-mass approximation. We have shown that the zeroth-order form of such formulations is just the well-known Born approximation, and the first-order form is completely equivalent to the extended Born approximation-based quasi-linear approximation. Hence, high-order approximations are proposed in this paper, which are given in closed forms. Using such approximations, good resolution images can be obtained for large-contrast objects by only solving a linear inverse scattering integral equation. Reconstruction examples show the validity and efficiency of the proposed formulae.