Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

We propose an inverse scattering scheme of recovering a polyhedral obstacle in Rn, n= 2, 3, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior, from which one can determine the exterior normal directions of the front sides/faces. Then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions, one can determine the exterior unit normal vector of each side/face of the obstacle. After the determination of the exterior unit normals, the recovery is reduced to a finite-dimensional problem of determining a location point of the obstacle and the distance of each side/face away from the location point. For the latter reconstruction, we need to make use of the far-field data with phases. Numerical experiments are also presented to illustrate the effectiveness of the proposed scheme.

Keywords

Backscattering, Inverse scattering, Phaseless, Polyhedral obstacle

Publication Date

9-2015

Source Publication Title

Journal of Differential Equations

Volume

259

Issue

5

Start Page

2101

End Page

2120

Publisher

Elsevier

Peer Reviewed

1

Copyright

Copyright © 2015 Elsevier Inc. All rights reserved.

Funder

This work was supported by the NSFC under the grants No. 11201453 and No. 11371115, and the FRG and startup funds from Hong Kong Baptist University.

DOI

10.1016/j.jde.2015.03.030

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jde.2015.03.030

ISSN (print)

00220396

Available for download on Sunday, October 01, 2017

Included in

Mathematics Commons

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