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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 18, Issue 2


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

Hélène Barucq
  • INRIA 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:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Chokri Bekkey / Rabia Djellouli
  • Corresponding author
  • Department of Mathematics, California State University Northridge & INRIA Bordeaux Sud-Ouest Research Center, Associate Team Project MAGIC, USA. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-05-31 | DOI: https://doi.org/10.1515/jiip.2010.007


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

About the article

Received: 2009-09-30

Published Online: 2010-05-31

Published in Print: 2010-05-01

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: https://doi.org/10.1515/jiip.2010.007.

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