Reconstruction of extended sources for the Helmholtz equation Academic Article

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.

authors

• Rundell, William

published proceedings

• INVERSE PROBLEMS

author list (cited authors)

• Kress, R., & Rundell, W.

citation count

• 10

complete list of authors

• Kress, Rainer||Rundell, William

publication date

• March 2013

publisher

• IOP Publishing  Publisher

published in

• Inverse Problems  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics
• Bioengineering
• Networking And Information Technology R&d (nitrd)

Digital Object Identifier (DOI)

• 10.1088/0266-5611/29/3/035005

start page

• 035005

end page

• 035005

volume

• 29

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1088%2F0266-5611%2F29%2F3%2F035005