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Fisher information analysis in electrical impedance tomography
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.ORCID iD: 0000-0002-7018-6248
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Lund University.
National Research Council.
2012 (English)In: Geophysical Research Abstract: EGU General Assembly 2012, 2012, 2012-3553-1- p.Conference paper, (Refereed)
Abstract [en]

In this contribution it is demonstrated how the Cramér-Rao lower bound provides a quantitative analysis of theoptimal accuracy and resolution in inverse imaging, see also Nordebo et al., 2010, 2010b, 2010c. The imagingproblem is characterized by the forward operator and its Jacobian. The Fisher information operator is defined fora deterministic parameter in a real Hilbert space and a stochastic measurement in a finite-dimensional complexHilbert space with Gaussian measure. The connection between the Fisher information and the Singular ValueDecomposition (SVD) based on the Maximum Likelihood (ML) criterion (the ML-based SVD) is established. Itis shown that the eigenspaces of the Fisher information provide a suitable basis to quantify the trade-off betweenthe accuracy and the resolution of the (non-linear) inverse problem. It is also shown that the truncated ML-basedpseudo-inverse is a suitable regularization strategy for a linearized problem, which exploits a sufficient statisticsfor estimation within these subspaces.The statistical-based Cramér-Rao lower bound provides a complement to the deterministic upper bounds and theL-curve techniques that are employed with linearized inversion (Kirsch, 1996; Hansen, 1992, 1998, 2010). To thisend, the Electrical Impedance Tomography (EIT) provides an interesting example where the eigenvalues of theSVD usually do not exhibit a very sharp cut-off, and a trade-off between the accuracy and the resolution may be ofpractical importance. A numerical study of EIT is described, including a statistical analysis of the model errors dueto the linearization. The Fisher information and sensitivity analysis is also used to compare, evaluate, and optimizemeasurement configurations in EIT.

Place, publisher, year, edition, pages
2012. 2012-3553-1- p.
National Category
Physical Sciences
Research subject
Natural Science, Physics
Identifiers
URN: urn:nbn:se:lnu:diva-19207OAI: oai:DiVA.org:lnu-19207DiVA: diva2:530061
Conference
European Geosciences Union General Assembly, Vienna, 22-27 April, 2012
Available from: 2012-05-31 Created: 2012-05-31 Last updated: 2017-01-10Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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Language
  • de-DE
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  • fi-FI
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