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 language | English (US) |
|---|---|
| Pages (from-to) | 185-202 |
| Number of pages | 18 |
| Journal | Inverse Problems and Imaging |
| Volume | 5 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 23 2011 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: This research was supported by the National Science Foundation under grant DMS-0715060 and by the King Abdullah University of Science and Technology (KAUST) award KUS-CI-016-04.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.