Stationary waves method for inverse scattering problems

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November 2008, 2(4): 577-586. doi: 10.3934/ipi.2008.2.577

Stationary waves method for inverse scattering problems

1.	Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Finland

Received July 2008 Revised August 2008 Published November 2008

Abstract
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We present a constructive algorithm, the stationary waves method, to get approximative reconstructions in the inverse scattering problems. The method is a version of the singular sources/probe method but the singular fields are replaced with the stationary waves. The suggested indicator function compromises in getting exactly the obstacle, but it is very easy and fast to compute, robust with noise, and seems to give excellent reconstruction images. The method is introduced in the context of the acoustic inverse obstacle scattering problems.

Keywords: numerical algorithm, Inverse scattering problem, reconstruction.

Mathematics Subject Classification: Primary: 78A46, 65R32; Secondary: 65N38.

Citation: Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems & Imaging, 2008, 2 (4) : 577-586. doi: 10.3934/ipi.2008.2.577

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