KAUST Grant NumberKUS-CI-016-04
Online Publication Date2013-02-26
Print Publication Date2013-03-01
Permanent link to this recordhttp://hdl.handle.net/10754/599467
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AbstractThe basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our inclusions are interior forces with compact support and our data consist of a single measurement of near-field Cauchy data on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler 'equivalent point source' problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2013 IOP Publishing Ltd.
CitationKress R, Rundell W (2013) Reconstruction of extended sources for the Helmholtz equation. Inverse Problems 29: 035005. Available: http://dx.doi.org/10.1088/0266-5611/29/3/035005.
SponsorsThis research was supported by the National Science Foundation under grant DMS-0715060 and by KAUST award KUS-CI-016-04. It was initiated while WR visited the University of Gottingen with the support of the SFB Nanoscale Photonic Imaging.