The shape of a plane acoustical sound-soft obstacle is detected from knowledge of the far field pattern for one time-harmonic incident field. Two methods based on solving a system of integral equations for the incoming wave and the far field pattern are investigated. Properties of the integral operators required in order to apply regularization, i.e. injectivity and denseness of the range, are proved.
Editor-in-Chief: Kabanikhin, Sergey I.
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Boundary integral equations for acoustical inverse sound-soft scattering
1 Institute for Numerical and Applied Mathematics, Georg-August University of Göttingen, Lotzestr. 16–18, Göttingen, Germany. Email: ivanyshy@math.uni-goettingen.de
2 School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. Email: b.t.johansson@bham.ac.uk
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 16, Issue 1, Pages 65–78, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2008.005, March 2008
Publication History:
- Received:
- 2006-11-03
- Published Online:
- 2008-03-05
Keywords: Far field pattern; ill-posed; inverse scattering; Newton method; sound-soft
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