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Proceedings Paper

Globally strictly convex cost functionals for search of land mines using electrical methods (Conference Presentation)
Author(s): Michael V. Klibanov D.D.S.

Paper Abstract

We formulate the problem of the search of land mines as the inverse scattering problem for the Helmholtz Partial Differential Equation. In this problem one is looking to find location, shape and dielectric constant of a mine or mine-like target or IED. The commonly known main challenge of numerical solution of such a problem is due to non-convexity of resulting least squares cost functional. The non-convexity causes the phenomenon of multiple local minima and ravines of this functional. We overcome this challenge, we construct a weighted globally strictly convex cost functional. Its weight is the so-called Carleman Weight Function, i.e. the function involved in the Carleman estimate for the corresponding Partial Differential Operator. We will present highly accurate results of testing of our method on experimental data for microwaves.

Paper Details

Date Published: 14 May 2019
Proc. SPIE 11012, Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XXIV, 110120H (14 May 2019); doi: 10.1117/12.2522833
Show Author Affiliations
Michael V. Klibanov D.D.S., The Univ. of North Carolina at Charlotte (United States)

Published in SPIE Proceedings Vol. 11012:
Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XXIV
Steven S. Bishop; Jason C. Isaacs, Editor(s)

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