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Full Aperture Reconstruction of the Acoustic Far-Field Pattern from Few Measurements

Published online by Cambridge University Press:  20 August 2015

Hélène Barucq ,
Chokri Bekkey  and
Rabia Djellouli
Hélène Barucq*
Affiliation:
INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D, & LMA/CNRS UMR 5142, Université de Pau et des Pays de l’Adour, France
Chokri Bekkey*
Affiliation:
Faculté des Sciences de Monastir, Tunisia
Rabia Djellouli*
Affiliation:
Department of Mathematics, California State University Northridge & Interdisciplinary Research Institute for the Sciences, IRIS, USA
*
Email address:helene.barucq@univ-pau.fr
Email address:chokri.bekkey@ipeit.rnu.tn
Corresponding author.Email:rabia.djellouli@csun.edu
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Abstract

We propose a numerical procedure to extend to full aperture the acoustic far-field pattern (FFP) when measured in only few observation angles. The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion. The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms. We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.

Keywords

35J0578A4674J2065F2265T4035N05Acoustic scattering problemlimited apertureinverse obstacle problemill-posed problemtotal variationTikhonov regularizationNewton method
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 647 - 659
Copyright
Copyright © Global Science Press Limited 2012

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