Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm

Abstract

Abstract.An approximately globally convergent numerical method for a 1-D Coefficient Inverse Problem for a hyperbolic PDE is applied to image dielectric constants of targets from blind experimental data. The data were collected in the field by the Forward Looking Radar of the US Army Research Laboratory. A posteriori analysis has revealed that computed and tabulated values of dielectric constants are in a good agreement. Convergence analysis is presented.1. Introduction. In this paper we test the 1-D version [31] of the numerical method of recent publications [5,6,7,8,9,10,11,12,27,28,32,48] for the case when the time resolved backscattering electric signal is measured experimentally in the field. Measurements were conducted by the Forward Looking Radar built in US Army Research Laboratory (ARL). All kinds of clutter were present at the site of data collection. The data are severely limited. The goal of this radar is to detect and possibly identify shallow explosive-like targets. Prior to this effort, the focus of the ARL team was on the image processing rather than on the target detection and identification [37]. The current data processing procedure of ARL delivers only the energy information. The algorithm of this paper computes values of dielectric constants of targets using those data. These values represent a new, surprising and quite useful dimension of information for the ARL team. A hope is that these values might be helpful in the target detection and identification process.The UNCC/ChalmersGU team has worked only with the most challenging case of blind experimental data. "Blind" means that first computations were made by the UNCC/ChalmersGU team without any knowledge of correct answers. Next, computational results were sent to the ARL team. The ARL team has compared a posteriori those results with the reality and then revealed correct answers to the UNCC/ChalmersGU team. The performance of the algorithm of above cited publications for transmitted blind experimental data was presented in [27], see Tables 5 and 6 there. Images of [27] were refined in the follow up publication [9] using the adaptivity technique of [3,4].In the above cited works a new numerical method was developed for some Multidimensional Coefficient Inverse Problems (MCIPs) for a hyperbolic PDE with single measurement data. "Single measurement" means that either only a single position of the point source or only a single direction of the incident plane wave is considered. Because of many dangers on the battlefield, the single measurement arrangement is the most suitable one for military applications. There were two goals of those publications: Goal 1. To develop such a numerical method, which would have a rigorous guarantee obtaining a good approximation for the exact solution of a CIP without using an advanced knowledge of neither a small neighborhood of that solution nor of the background medium in the domain of interest.Goal 2. This method should demonstrate a good performance on both computationally simulated and experimental data....

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

“…We only remark that unlike certain applications, e.g. some significant mismatch has been reported in [1,23,27] between experimental data of electromagnetic waves propagating in a non-attenuating medium and data produced by idealized computational simulations, in inverse heat conduction the mathematical models have been shown to perform much better in industrial applications with actual real measured data, [9]. 30, 025002 (24 pages).…”

A globally convergent numerical method for a coefficient inverse problem for a parabolic equation

“…However, it might be possible to invent such a method which would satisfy the requirement (a) for at least one MCIP. The latter was done in works of Klibanov in 2008-2014 [1][2][3][4][5][6][7][8]. Furthermore, their method was completely verified on experimental data [3][4][5][6][7][8].…”

“…Thus, we can assume that the function g(x, t) is known at the entire surface, see, e.g. a similar situation for the case of real measurements in [3][4][5][6][7][8]. We do not discuss here a specific way of that interpolation.…”

“…where the function g was defined in (5). Also, the following asymptotic behavior of w(x, s) holds [18]:…”

“…The latter was done in works of Klibanov in 2008-2014 [1][2][3][4][5][6][7][8]. Furthermore, their method was completely verified on experimental data [3][4][5][6][7][8]. Recently Chow and Zou [9] have studied the Beilina-Klibanov method numerically for a MCIP for a hyperbolic equation, which is different from the one studied in [1][2][3][4][5][6][7][8].…”