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A Green's function approach to Fisher information analysis and preconditioning in microwave 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.
2010 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 18, no 8, p. 1043-1063Article in journal (Refereed) Published
Abstract [en]

The Fisher Information Integral Operator (FIO) and related sensitivity analysis is formulated in a variational framework that is suitable for analytical Green's function and gradient-based approaches in microwave tomography. The main application considered here is for parameter sensitivity analysis and related preconditioning for gradient-based quasi-Newton inverse scattering algorithms. In particular, the Fisher information analysis can be used as a basic principle yielding a systematic approach to robust preconditioning, where the diagonal elements of the FIO kernel are used as targets for sensitivity equalization. The infinite-dimensional formulation has several practical advantages over the finite-dimensional Fisher Information Matrix (FIM) analysis approach. In particular, the FIO approach avoids the need of making a priori assumptions about the underlying discretization of the material such as the shape, orientation and positions of the assumed image pixels. Furthermore, the integral operator and its spectrum can be efficiently approximated by using suitable quadrature methods for numerical integration. The eigenfunctions of the integral operator, corresponding to the identifiable parameters via the significant eigenvalues and the corresponding Cramr-Rao bounds, constitute a suitable global basis for sensitivity and resolution analysis. As a generic numerical example, a two-dimensional inverse electromagnetic scattering problem is analysed and illustrates the spectral decomposition and the related resolution analysis. As an application example in microwave tomography, a simulation study has been performed to illustrate the parameter sensitivity analysis and to demonstrate the effect of the related preconditioning for gradient-based quasi-Newton inverse scattering algorithms.

Place, publisher, year, edition, pages
2010. Vol. 18, no 8, p. 1043-1063
National Category
Physical Sciences
Research subject
Physics, Waves and Signals
Identifiers
URN: urn:nbn:se:lnu:diva-7095DOI: 10.1080/17415977.2010.513437Scopus ID: 2-s2.0-78649803221OAI: oai:DiVA.org:lnu-7095DiVA, id: diva2:342743
Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Nordebo, SvenNilsson, Börje

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