Fisher information analysis in electrical impedance tomography
(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:
https://lup.lub.lu.se/record/4178297
- author
- Nordebo, Sven LU ; Gustafsson, Mats LU ; Nilsson, Börje ; Sjöden, Therese and Soldovieri, Francesco
- organization
- publishing date
- 2013
- 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}}, }