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....

A globally convergent algorithm of the first and third authors for a 3D hyperbolic coefficient inverse problem is verified on experimental data measured in the picosecond scale regime. Quantifiable images of dielectric abnormalities are obtained. The total measurement timing of a 100 pico-seconds pulse for one detector location was 1.2 nano-second with 20 pico-seconds (0.02 nano-second) time step between two consequtive readings. Blind tests have consistently demonstrated an accurate imaging of refractive indexes of dielectric abnormalities. At the same time, it is shown that a modified gradient method is inapplicable to this kind of experimental data. This inverse algorithm is also applicable to other types of imaging modalities, e.g. acoustics. Potential applications are in airport security, imaging of land mines, imaging of defects in non-distractive testing, etc..

The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric constant) of an inhomogeneous medium using one backscattering boundary measurement. The goal of this paper is to analyze the performance of a globally convergent algorithm of Beilina and Klibanov on experimental data acquired in the Microwave Laboratory at University of North Carolina at Charlotte. The main challenge working with experimental data is the the huge misfit between these data and computationally simulated data. We present data pre-processing steps to make the former somehow look similar to the latter. Results of both non-blind and blind targets are shown indicating good reconstructions even for high contrasts between the targets and the background medium.

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We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. The challenges for the inverse problem under the consideration are not only from its high nonlinearity and severe ill-posedness but also from the facts that the amount of the measured data is minimal and that these raw data are contaminated by a significant amount of noise, due to a non-ideal experimental setup. This setup is motivated by our target application in detecting and identifying explosives. We show in this paper how the raw data can be preprocessed and successfully inverted using our inversion method. More precisely, we are able to reconstruct the dielectric constants and the locations of the scattering objects with a good accuracy, without using any advanced a priori knowledge of their physical and geometrical properties.