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

Hélène Barucq 1, 2 Rabia Djellouli 3 Chokri Bekkey 4
1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
3 Department of Mathematics [CSUN]
4 Département de Mathématiques [Monastir]
Abstract : 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 !=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.
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Submitted on : Monday, October 18, 2010 - 4:30:38 PM
Last modification on : Wednesday, July 24, 2019 - 4:02:06 PM

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Hélène Barucq, Rabia Djellouli, Chokri Bekkey. A multi-step procedure for enriching limited two-dimensional acoustic far-field pattern measurements. Journal of Inverse and Ill-posed Problems, De Gruyter, 2010, 18 (2), pp.189-216. ⟨10.1515/jiip.2010.007⟩. ⟨inria-00527273⟩

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