`a`
Inverse Problems and Imaging (IPI)
 

Identification of sound-soft 3D obstacles from phaseless data

Pages: 131 - 149, Volume 4, Issue 1, February 2010

doi:10.3934/ipi.2010.4.131       Abstract        Full Text (929.9K)       Related Articles

Olha Ivanyshyn - Institut für Numerische und Angewandte Mathematik, University of Göttingen, Lotzestr. 16-18, 37083, Göttingen, Germany (email)
Rainer Kress - Institut für Numerische und Angewandte Mathematik, University of Göttingen, Lotzestr. 16-18, 37083, Göttingen, Germany (email)

Abstract: The inverse problem for time-harmonic acoustic wave scattering to recover a sound-soft obstacle from a given incident field and the far field pattern of the scattered field is considered. We split this problem into two subproblems; first to reconstruct the shape from the modulus of the data and this is followed by employing the full far field pattern in a few measurement points to find the location of the obstacle. We extend a nonlinear integral equation approach for shape reconstruction from the modulus of the far field data [6] to the three-dimensional case. It is known, see [13], that the location of the obstacle cannot be reconstructed from only the modulus of the far field pattern since it is invariant under translations. However, employing the underlying invariance relation and using only few far field measurements in the backscattering direction we propose a novel approach for the localization of the obstacle. The efficient implementation of the method is described and the feasibility of the approach is illustrated by numerical examples.

Keywords:  Acoustic Scattering, Inverse Problem, Modulus of Far Field, Nonlinear Integral Equations, 3D.
Mathematics Subject Classification:  35R30, 78A46.

Received: May 2009;      Revised: November 2009;      Published: February 2010.