| 1. |
- Kuzhuget, A. V., et al.
(författare)
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Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm
- 2012
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 28:9
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Tidskriftsartikel (refereegranskat)abstract
- An approximately globally convergent numerical method for a 1D 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 good agreement. Convergence analysis is presented.
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| 2. |
- Kuzhuget, A. V., et al.
(författare)
-
Quantitative image recovery from measured blind backscattered data using a globally convergent inverse method
- 2013
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Ingår i: IEEE Transactions on Geoscience and Remote Sensing. - 0196-2892 .- 1558-0644. ; 51:5, s. 2937 - 2948
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Tidskriftsartikel (refereegranskat)abstract
- The goal of this paper is to introduce the application of a globally convergent inverse scattering algorithm to estimate dielectric constants of targets using time-resolved backscattering data collected by a U.S. Army Research Laboratory forward-looking radar. The processing of the data was conducted blind, i.e., without any prior knowledge of the targets. The problem is solved by formulating the scattering problem as a coefficient inverse problem for a hyperbolic partial differential equation. The main new feature of this algorithm is its rigorously established global convergence property. Calculated values of dielectric constants are in a good agreement with material properties, which were revealed a posteriori.
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| 3. |
- Beilina, Larisa, 1970, et al.
(författare)
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New a posteriori error estimates for adaptivity technique and global convergence for a hyperbolic coefficient inverse problem
- 2011
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Ingår i: Journal of Mathematical Sciences. - : Springer Science and Business Media LLC. - 1573-8795 .- 1072-3374. ; 172:4, s. 449-476
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Tidskriftsartikel (refereegranskat)abstract
- The coefficient inverse problem for a hyperbolic equation is studied by using the two-stage numerical procedure consisting of the global convergence method and the adaptive finite element method. We obtain new a posteriori error estimates for the Lagrangian and for the unknown coefficient, which is important at the second stage of procedure from the computational point of view. The results are illustrated by numerical experiments. Bibliography: 23 titles. Illustrations: figures. © 2011 Springer Science+Business Media, Inc.
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| 4. |
- Kuzhuget, A. V., et al.
(författare)
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Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data
- 2012
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Ingår i: Journal of Mathematical Sciences. - : Springer Science and Business Media LLC. - 1072-3374 .- 1573-8795. ; 181:2, s. 126-163
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Tidskriftsartikel (refereegranskat)abstract
- A numerical method possessing the approximate global convergence property is developed for a 3-D coefficient inverse problem for hyperbolic partial differential equations with backscattering data resulting from a single measurement. An important part of this technique is the quasireversibility method. An approximate global convergence theorem is proved. Results of two numerical experiments are presented.
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| 5. |
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