Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method

Abstract

This paper is concerned with the numerical solution to a 3D coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave, are backscatter data for targets buried in a sandbox. These raw scattering data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. We develop a data preprocessing procedure and exploit a newly developed globally convergent inversion method for solving the inverse problem with these preprocessed data. It is shown that dielectric constants of the buried targets as well as their locations are reconstructed with a very good accuracy. We also prove a new analytical result which rigorously justifies an important step of the so-called "data propagation" procedure.

Convexification Method for an Inverse Scattering Problem and Its Performance for Experimental Backscatter Data for Buried Targets

“…In Table 2 we present the optimal frequencies and corresponding intervals of wavenumbers [k, k] for our objects. We refer to [35] for the details of the determination of these intervals.…”

“…For the convenience of the readers we briefly summarize the main steps of the data preprocessing developed in [35].…”

“…The numerical method we develop in this paper can be considered as the second type of GCMs, which has certain advantages compared with the first type of GCMs in [6,35,36]. More precisely, we do not impose in the convergence analysis here the assumption on a small interval of wavenumbers.…”

A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

“…This problem is solved below by the globally convergent numerical method, which was developed in [38]. As it was mentioned in Section 1, this method was successfully tested on microwave experimental data in [46,54,53].…”

“…It is on the second stage when we reconstruct locations and refractive indices of those microspheres. The numerical solution of the phased CIP is found using the globally convergent numerical method, which was recently developed in [38], also, see [46,54,53] for the performance of this method on microwave experimental backscattering data Our interest in phaseless CIPs is motivated by applications to optical imaging of such small objects as, e.g. biological cells and microspheres.…”