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Fisher information analysis in electrical impedance tomography

Nordebo, Sven LU ; Gustafsson, Mats LU orcid ; Nilsson, Börje ; Sjöden, Therese and Soldovieri, Francesco (2013) In Journal of Geophysics and Engineering 10(6).
Abstract
This paper provides a quantitative analysis of the optimal accuracy and resolution in electrical impedance tomography (EIT) based on the Cramér–Rao lower bound. The imaging problem is characterized by the forward operator and its Jacobian. The Fisher information operator is defined for a deterministic parameter in a real Hilbert space and a stochastic measurement in a finite-dimensional complex Hilbert space with a Gaussian measure. The connection between the Fisher information and the singular value decomposition (SVD) based on the maximum likelihood (ML) criterion (the ML-based SVD) is established. It is shown that the eigenspaces of the Fisher information provide a suitable basis to quantify the trade-off between the accuracy and the... (More)
This paper provides a quantitative analysis of the optimal accuracy and resolution in electrical impedance tomography (EIT) based on the Cramér–Rao lower bound. The imaging problem is characterized by the forward operator and its Jacobian. The Fisher information operator is defined for a deterministic parameter in a real Hilbert space and a stochastic measurement in a finite-dimensional complex Hilbert space with a Gaussian measure. The connection between the Fisher information and the singular value decomposition (SVD) based on the maximum likelihood (ML) criterion (the ML-based SVD) is established. It is shown that the eigenspaces of the Fisher information provide a suitable basis to quantify the trade-off between the accuracy and the resolution of the (nonlinear) inverse problem. It is also shown that the truncated ML-based pseudo-inverse is a suitable regularization strategy for a linearized problem, which exploits sufficient statistics for estimation within these subspaces. The statistical-based Cramér–Rao lower bound provides a complement to the deterministic upper bounds and the L-curve techniques that are employed with linearized inversion. To this end, electrical impedance tomography provides an interesting example where the eigenvalues of the SVD usually do not exhibit a very sharp cut-off, and a trade-off between the accuracy and the resolution may be of practical importance. A numerical study of a hypothetical EIT problem is described, including a statistical analysis of the model errors due to the linearization. (Less)
Please use this url to cite or link to this publication:
author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Geophysics and Engineering
volume
10
issue
6
article number
064008
publisher
IOP Publishing
external identifiers
  • wos:000334994600009
  • scopus:84893496491
ISSN
1742-2140
DOI
10.1088/1742-2132/10/6/064008
project
EIT_ISTIMES Integrated System for Transport Infrastructures surveillance and Monitoring by Electromagnetic Sensing
language
English
LU publication?
yes
id
6a4509b9-b38c-47e5-b2c3-191e4f89bbe4 (old id 4178297)
date added to LUP
2016-04-01 10:31:27
date last changed
2022-01-25 23:59:59
@article{6a4509b9-b38c-47e5-b2c3-191e4f89bbe4,
  abstract     = {{This paper provides a quantitative analysis of the optimal accuracy and resolution in electrical impedance tomography (EIT) based on the Cramér–Rao lower bound. The imaging problem is characterized by the forward operator and its Jacobian. The Fisher information operator is defined for a deterministic parameter in a real Hilbert space and a stochastic measurement in a finite-dimensional complex Hilbert space with a Gaussian measure. The connection between the Fisher information and the singular value decomposition (SVD) based on the maximum likelihood (ML) criterion (the ML-based SVD) is established. It is shown that the eigenspaces of the Fisher information provide a suitable basis to quantify the trade-off between the accuracy and the resolution of the (nonlinear) inverse problem. It is also shown that the truncated ML-based pseudo-inverse is a suitable regularization strategy for a linearized problem, which exploits sufficient statistics for estimation within these subspaces. The statistical-based Cramér–Rao lower bound provides a complement to the deterministic upper bounds and the L-curve techniques that are employed with linearized inversion. To this end, electrical impedance tomography provides an interesting example where the eigenvalues of the SVD usually do not exhibit a very sharp cut-off, and a trade-off between the accuracy and the resolution may be of practical importance. A numerical study of a hypothetical EIT problem is described, including a statistical analysis of the model errors due to the linearization.}},
  author       = {{Nordebo, Sven and Gustafsson, Mats and Nilsson, Börje and Sjöden, Therese and Soldovieri, Francesco}},
  issn         = {{1742-2140}},
  language     = {{eng}},
  number       = {{6}},
  publisher    = {{IOP Publishing}},
  series       = {{Journal of Geophysics and Engineering}},
  title        = {{Fisher information analysis in electrical impedance tomography}},
  url          = {{http://dx.doi.org/10.1088/1742-2132/10/6/064008}},
  doi          = {{10.1088/1742-2132/10/6/064008}},
  volume       = {{10}},
  year         = {{2013}},
}