Commun. Comput. Phys., 11 (2012), pp. 647-659.

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

Helene Barucq 1, Chokri Bekkey 2, Rabia Djellouli 3*

1 INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D, and LMA/CNRS UMR 5142, Universite de Pau et des Pays de l'Adour, France.
2 Faculte des Sciences de Monastir, Tunisia.
3 Department of Mathematics, California State University Northridge and Interdisciplinary Research Institute for the Sciences, IRIS, USA.

Received 28 December 2009; Accepted (in revised version) 15 June 2010
Available online 24 October 2011


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.

AMS subject classifications: 35J05, 78A46, 74J20, 65F22, 65T40, 35N05

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Key words: Acoustic scattering problem, limited aperture, inverse obstacle problem, ill-posed problem, total variation, Tikhonov regularization, Newton method.

*Corresponding author.
Email: (H. Barucq), (C. Bekkey), (R. Djellouli)

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