Microwave imaging in the time domain of buried multiple scatterers by using an FDTD-based optimization technique

In this paper, a microwave imaging technique for reconstructing underground multiple scatterers is presented. The electromagnetic properties of buried objects are estimated by postprocessing total-field measurements, which are obtained when the domain of investigation is illuminated by wide-band electromagnetic waves. The solution of this limited-angle inverse scattering problem is based on the differential formulation of the direct problem. The scatterers are reconstructed by applying an iterative technique, which combines the finite-difference time-domain (FDTD) method and the Polak-Ribiere optimization algorithm. An augmented cost functional is defined taking into account the fulfillment of the Maxwell´s curl equations by means of Lagrange multipliers. The Frechet derivatives of the functional with respect to the scatterer properties are derived from the stationary condition. Moreover, it is proven that the Lagrange multipliers fulfill the Maxwell´s curl equations. In numerical results, the presented technique is applied to the reconstruction of scatterers buried in earth. In general, these scatterers can be dielectric, lossy, or magnetic.