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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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A multi-step procedure for enriching limited two-dimensional acoustic far-field pattern measurements

Hélène Barucq1 / Chokri Bekkey2 / Rabia Djellouli3

1INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D, & LMA/CNRS UMR 5142, Université de Pau et des Pays de l'Adour, France. E-mail:

2Faculté des Sciences de Monastir, Tunisia. E-mail:

3Department of Mathematics, California State University Northridge & INRIA Bordeaux Sud-Ouest Research Center, Associate Team Project MAGIC, USA. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 2, Pages 189–216, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2010.007, May 2010

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We propose a three-step solution methodology to increase the discrete set of acoustic far-field pattern (FFP) measurements, available in a small range of observation angles (small aperture). The first two steps of the proposed procedure allow the extension of the data to an aperture larger than π/2. They use a regularized Newton algorithm where the total variation of the FFP is incorporated as a regularization term. The third step consists in applying the standard Tikhonov regularization technique to recover the full aperture of the FFP from the previously extended field. Numerical results obtained using synthetic data illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from data given in an aperture as small as backscattering measurements.

Keywords.: Acoustic scattering problem; limited aperture; inverse obstacle problem; ill-posed problem; total variation; Tikhonov regularization; Newton method

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