Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792
CiteScore 2016: 0.80
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Source Normalized Impact per Paper (SNIP) 2015: 1.106
Mathematical Citation Quotient (MCQ) 2015: 0.43
A multi-step procedure for enriching limited two-dimensional acoustic far-field pattern measurements
- 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: firstname.lastname@example.org
- Faculté des Sciences de Monastir, Tunisia. E-mail: email@example.com
- Corresponding author
- Department of Mathematics, California State University Northridge & INRIA Bordeaux Sud-Ouest Research Center, Associate Team Project MAGIC, USA. E-mail: firstname.lastname@example.org
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.