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| Titel |
Fisher information analysis in electrical impedance tomography |
| VerfasserIn |
S. Nordebo, T. Sjödén, M. Gustafsson, F. Soldovieri |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250061521
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| Zusammenfassung |
| In this contribution it is demonstrated how the Cramér-Rao lower bound provides a
quantitative analysis of the optimal accuracy and resolution in inverse imaging, see also
Nordebo et al., 2010, 2010b, 2010c. 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 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 (non-linear) inverse problem. It is also shown
that the truncated ML-based pseudo-inverse is a suitable regularization strategy for a
linearized problem, which exploits a 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 (Kirsch, 1996; Hansen, 1992, 1998, 2010). To this end, the Electrical Impedance
Tomography (EIT) 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 EIT is described, including a statistical
analysis of the model errors due to the linearization. The Fisher information and sensitivity
analysis is also used to compare, evaluate, and optimize measurement configurations in
EIT.
Acknowledgement
The research leading to these results has received funding from the European Community’s
Seventh Framework Programme (FP7/2007-2013) under Grant Agreement no 225663.
References
[1]   S. Nordebo, A. Fhager, M. Gustafsson, and B. Nilsson. A Green’s function
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