Globally convergent and adaptive finite element methods in imaging of   buried objects from experimental backscattering radar measurements
  We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte. Our imaging problem is formulated as the inverse problem of the reconstruction of the spatially distributed dielectric permittivity $\varepsilon_\mathrm{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in Maxwell's equations.   On the first stage an approximately globally convergent method is applied to get a good first approximation for the exact solution. On the second stage a local adaptive finite element method is applied to refine the solution obtained on the first stage. The two-stage numerical procedure results in accurate imaging of all three components of interest of targets: shapes, locations and refractive indices. In this paper we briefly describe methods and present new reconstruction results for both stages. 
Larisa Beilina, Nguyen Trung Th\`anh, Michael V. Klibanov and John   Bondestam Malmberg
math.NA