TY - JOUR
T1 - On rational approximation methods for inverse source problems
AU - Rundell, William
AU - Hanke, Martin
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged 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.
PY - 2011/2/23
Y1 - 2011/2/23
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/599043
UR - http://aimsciences.org//article/doi/10.3934/ipi.2011.5.185
UR - http://www.scopus.com/inward/record.url?scp=79951733714&partnerID=8YFLogxK
U2 - 10.3934/ipi.2011.5.185
DO - 10.3934/ipi.2011.5.185
M3 - Article
SN - 1930-8337
VL - 5
SP - 185
EP - 202
JO - Inverse Problems and Imaging
JF - Inverse Problems and Imaging
IS - 1
ER -