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Published in:
Iteratively Regularized Gauss-Newton Methods under Random Noise Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Methods of Quantitative Reconstruction of Shapes and Refractive Indices from Experimental data

Authors : Larisa Beilina, Nguyen Trung Thành, Michael V. Klibanov, John Bondestam Malmberg

Published in: Inverse Problems and Applications

Publisher: Springer International Publishing

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Abstract

In this chapter we summarize results of [5, 6, 14] and present new results of reconstruction of refractive indices and shapes of objects placed in the air from blind backscattered experimental data using two-stage numerical procedure of [4]. Data are collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte.
On the first stage the approximately globally convergent method of [4] is applied to get a good first approximation for the exact solution. Results of this stage are presented in [5, 14]. On the second stage the local adaptive finite element method of [1] is applied to refine the solution obtained on the first stage. In this chapter we briefly describe methods and present new results for both stages.

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previous chapter Iteratively Regularized Gauss-Newton Methods under Random Noise
next chapter A Posteriori Error Estimate in the Lagrangian Setting for an Inverse Problem Based on a New Formulation of Maxwell’s System
Literature
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Beilina, L., Thành, N.T., Klibanov, M.V., Fiddy, M.A.: Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation. Inv. Probl. 30, 02500–2. (2014). doi:10.1088/0266-5611/30/2/025002
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Thành, N.T., Beilina, L., Klibanov, M.V., Fiddy, M.A.: Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method. SIAM J. Scientific Comput. 36, B273–B293 (2014)CrossRefMATH
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Metadata
Title
Methods of Quantitative Reconstruction of Shapes and Refractive Indices from Experimental data
Authors
Larisa Beilina
Nguyen Trung Thành
Michael V. Klibanov
John Bondestam Malmberg
Copyright Year
2015
Book
Inverse Problems and Applications

Print ISBN: 978-3-319-12498-8

Electronic ISBN: 978-3-319-12499-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12499-5_2

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