Reconstruction of extended sources for the Helmholtz equation

Rainer Kress, William Rundell

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

The 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.
Original languageEnglish (US)
Pages (from-to)035005
JournalInverse Problems
Volume29
Issue number3
DOIs
StatePublished - Feb 26 2013
Externally publishedYes

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