Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm

• Published in: Journal of computational physics 2017-09, Vol.345, p.17-32
• Main Authors: Nguyen, Dinh-Liem, Klibanov, Michael V., Nguyen, Loc H., Kolesov, Aleksandr E., Fiddy, Michael A., Liu, Hui
• Format: Article
• Language: English
• Subjects: Algorithms; Backscatter data; Backscattering; Binary system; Coefficient inverse problem; Computational physics; Convergence; Experimental multi-frequency data; Explosives detection; Fractions; Globally convergent numerical methods; Incident waves; Inverse problems; Microwave scattering; Numerical methods; Raw data; Target detection; Thermodynamics
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.05.015

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.