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

TL;DR

This paper presents a two-stage numerical approach combining a globally convergent method and adaptive finite element refinement for accurate imaging of buried objects using experimental radar data, effectively reconstructing shapes, locations, and dielectric properties.

Contribution

The paper introduces a novel two-stage procedure that integrates global convergence and adaptive refinement for improved imaging of buried objects from experimental radar measurements.

Findings

Successful reconstruction of shapes, locations, and dielectric properties of targets.

Effective combination of global and local methods enhances imaging accuracy.

Validation with experimental data demonstrates practical applicability.

Abstract

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.