Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements

摘要

We consider a two-stage numerical procedure for imaging of objects buried indry sand using time-dependent backscattering experimental radar measurements.These measurements are generated by a single point source of electric pulsesand are collected using a microwave scattering facility which was built at theUniversity of North Carolina at Charlotte. Our imaging problem is formulated asthe inverse problem of the reconstruction of the spatially distributeddielectric permittivity $\varepsilon_\mathrm{r}\left(\mathbf{x}\right), \\mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in Maxwell'sequations. On the first stage an approximately globally convergent method is applied toget a good first approximation for the exact solution. On the second stage alocal adaptive finite element method is applied to refine the solution obtainedon the first stage. The two-stage numerical procedure results in accurateimaging of all three components of interest of targets: shapes, locations andrefractive indices. In this paper we briefly describe methods and present newreconstruction results for both stages.