Reconstruction of extended sources for the Helmholtz equation

Handle URI:
http://hdl.handle.net/10754/599467
Title:
Reconstruction of extended sources for the Helmholtz equation
Authors:
Kress, Rainer; Rundell, William
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.
Citation:
Kress 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.
Publisher:
IOP Publishing
Journal:
Inverse Problems
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
26-Feb-2013
DOI:
10.1088/0266-5611/29/3/035005
Type:
Article
ISSN:
0266-5611; 1361-6420
Sponsors:
This 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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorKress, Raineren
dc.contributor.authorRundell, Williamen
dc.date.accessioned2016-02-28T05:51:41Zen
dc.date.available2016-02-28T05:51:41Zen
dc.date.issued2013-02-26en
dc.identifier.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.en
dc.identifier.issn0266-5611en
dc.identifier.issn1361-6420en
dc.identifier.doi10.1088/0266-5611/29/3/035005en
dc.identifier.urihttp://hdl.handle.net/10754/599467en
dc.description.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.en
dc.description.sponsorshipThis 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.en
dc.publisherIOP Publishingen
dc.titleReconstruction of extended sources for the Helmholtz equationen
dc.typeArticleen
dc.identifier.journalInverse Problemsen
dc.contributor.institutionUniversitat Gottingen, Gottingen, Germanyen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-CI-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.