On rational approximation methods for inverse source problems

William Rundell, Martin Hanke

Research output: Contribution to journalArticlepeer-review

25 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. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux 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. © 2011 American Institute of Mathematical Sciences.
Original languageEnglish (US)
Pages (from-to)185-202
Number of pages18
JournalInverse Problems and Imaging
Volume5
Issue number1
DOIs
StatePublished - Feb 23 2011
Externally publishedYes

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