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Inverse Problem for a Planar Conductivity Inclusion*

Choi, Doosung ; Helsing, Johan LU ; Kang, Sangwoo and Lim, Mikyoung (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.

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author
; ; and
organization
publishing date
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}},
}