Electromagnetic imaging of underground targets using constrained optimization

Several high-frequency electromagnetic techniques have been used in recent years to detect and identify buried objects. Post-processing of the collected data is performed in many of these techniques to obtain high-quality images of buried targets. Accurate reconstructions of the target´s constitutive parameters can be obtained by casting the imaging problem in terms of an inverse electromagnetic scattering problem. A number of techniques have been put forth recently to invert the electromagnetic data to obtain such images. The authors use a frequency-domain Born iterative method to reconstruct images of shallow targets. The Born iterative technique requires successive solutions to a forward scattering problem followed by an inverse scattering problem at each iteration step. They use a finite-difference time-domain (FDTD) algorithm to solve the forward scattering problem and constrained optimization for the inverse problem. Two-dimensional simulated data for several canonical objects buried in the ground are obtained using the FDTD technique. The same FDTD code is also used in calculating the Green´s function required for solving the constrained optimization problem. Lossy, inhomogeneous ground models are used in several simulations to illustrate the use of this technique for practical situations. The inversion process can be used to reconstruct images for many realistic dielectric contrasts for which a linear Born approximation fails. Moreover, it is also shown that a small number of measurements results in accurate reconstructions with this technique. Use of multiple frequencies is also investigated