The Kirsch-Kress method for inverse scattering by infinite locally rough interfaces

This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems...

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Bibliographic Details
Published in:Applicable analysis Vol. 96; no. 1; pp. 85 - 107
Main Authors: Li, Jianliang, Sun, Guanying, Zhang, Bo
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.01.2017
Taylor & Francis Ltd
Subjects:
Algorithms
Convergence
Helmholtz equation
Inverse
Inverse problems
Inverse scattering
Inversions
locally rough interface
Nonlinear programming
Optimization
Regularization
Scattering
Segments
the Kirsch-Kress approach
transmission problem
ISSN:0003-6811, 1563-504X
Online Access:Get full text
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Summary:This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems to the above inverse transmission problem with unbounded interfaces. To this end, we reformulate our inverse problem as a nonlinear optimization problem with a Tikhonov regularization term. We prove the convergence of the optimization problem when the regularization parameter tends to zero. Finally, numerical experiments are carried out to show the validity of the inversion algorithm.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2016.1192141