Inverse Problem for a Planar Conductivity Inclusion*
(2023) In SIAM Journal on Imaging Sciences 16(2). p.969-995- Abstract
This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous inclusion with arbitrary constant conductivity. The primary outcome of recovering a homogeneous inclusion is an inversion formula in terms of the GPTs for conformal mapping coefficients associated with the inclusion. To prove the formula, we establish matrix factorizations for the GPTs.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f6368a16-b29f-49b2-b03f-f4c5d40ca830
- author
- Choi, Doosung ; Helsing, Johan LU ; Kang, Sangwoo and Lim, Mikyoung
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- conformal mapping, generalized polarization tensor, inverse conductivity problem, Lipschitz domain
- in
- SIAM Journal on Imaging Sciences
- volume
- 16
- issue
- 2
- pages
- 27 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:85179182287
- ISSN
- 1936-4954
- DOI
- 10.1137/22M1522395
- language
- English
- LU publication?
- yes
- id
- f6368a16-b29f-49b2-b03f-f4c5d40ca830
- date added to LUP
- 2024-01-11 10:58:44
- date last changed
- 2024-01-11 10:58:44
@article{f6368a16-b29f-49b2-b03f-f4c5d40ca830, abstract = {{<p>This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous inclusion with arbitrary constant conductivity. The primary outcome of recovering a homogeneous inclusion is an inversion formula in terms of the GPTs for conformal mapping coefficients associated with the inclusion. To prove the formula, we establish matrix factorizations for the GPTs.</p>}}, author = {{Choi, Doosung and Helsing, Johan and Kang, Sangwoo and Lim, Mikyoung}}, issn = {{1936-4954}}, keywords = {{conformal mapping; generalized polarization tensor; inverse conductivity problem; Lipschitz domain}}, language = {{eng}}, number = {{2}}, pages = {{969--995}}, publisher = {{Society for Industrial and Applied Mathematics}}, series = {{SIAM Journal on Imaging Sciences}}, title = {{Inverse Problem for a Planar Conductivity Inclusion<sup>*</sup>}}, url = {{http://dx.doi.org/10.1137/22M1522395}}, doi = {{10.1137/22M1522395}}, volume = {{16}}, year = {{2023}}, }