Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

Wallacher, E.; Louis, A. K.

doi:https://doi.org/10.1155/IJBI/2006/93074

International Journal of Biomedical Imaging

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Volume 2006 | Article ID 093074 | https://doi.org/10.1155/IJBI/2006/93074

Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

E. Wallacher¹and A. K. Louis¹

Academic Editor: Freek Beekman

Received24 Mar 2006

Revised12 Oct 2006

Accepted12 Oct 2006

Published09 Jan 2007

Abstract

Many algorithms applied in inverse scattering problems use source-field systems instead of the direct computation of the unknown scatterer. It is well known that the resulting source problem does not have a unique solution, since certain parts of the source totally vanish outside of the reconstruction area. This paper provides for the two-dimensional case special sets of functions, which include all radiating and all nonradiating parts of the source. These sets are used to solve an acoustic inverse problem in two steps. The problem under discussion consists of determining an inhomogeneous obstacle supported in a part of a disc, from data, known for a subset of a two-dimensional circle. In a first step, the radiating parts are computed by solving a linear problem. The second step is nonlinear and consists of determining the nonradiating parts.

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Copyright

Copyright © 2006 E. Wallacher and A. K. Louis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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