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Fisher information analysis in electrical impedance tomography

På svenska

Author

  • Sven Nordebo
  • Mats Gustafsson
  • Börje Nilsson
  • Therese Sjöden
  • Francesco Soldovieri

Summary, in English

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.

Publishing year

2013

Language

English

Publication/Series

Journal of Geophysics and Engineering

Volume

10

Issue

6

Document type

Journal article

Publisher

IOP Publishing

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Status

Published

Project

  • EIT_ISTIMES Integrated System for Transport Infrastructures surveillance and Monitoring by Electromagnetic Sensing

Research group

  • Electromagnetic theory

ISBN/ISSN/Other

  • ISSN: 1742-2140