| 11. |
- Nordebo, Sven, et al.
(author)
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Fisher information analysis and preconditioning in electrical impedance tomography
- 2010
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In: Journal of Physics: Conference Series 224 (2010), 1742-6588. - : IOP Publishing. - 1742-6596 .- 1742-6588. ; , s. 012057-
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Conference paper (peer-reviewed)abstract
- An adjoint field approach is used to formulate a general numerical framework for Fisher information based sensitivity analysis in electrical impedance tomography. General expressions are given for the gradients used in standard least squares optimization, i.e., the Jacobian related to the forward problem, and it is shown that these gradient expressions are consistent with commonly used electrode models such as the shunt model and the complete electrode model. By using the adjoint field formulations together with a variational analysis, it is also shown how the computation of the Fisher information can be integrated with the gradient calculations used for optimization. It is furthermore described how the Fisher information analysis and the related sensitivity map can be used in a preconditioning strategy to obtain a well balanced parameter sensitivity and improved performance for gradient based quasi-Newton optimization algorithms in electrical impedance tomography. Numerical simulations as well as reconstructions based on experimental data are used to illustrate the sensitivity analysis and the performance of the improved inversion algorithm in a four-electrode measurement set-up.
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| 12. |
- Nordebo, Sven, et al.
(author)
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Fisher information analysis in electrical impedance tomography
- 2013
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In: Journal of Geophysics and Engineering. - : Institute of Physics (IOP). - 1742-2132 .- 1742-2140. ; 10:6, s. Article ID: 064008-
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Journal article (peer-reviewed)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.
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| 13. |
- Nordebo, Sven, et al.
(author)
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Fisher information for inverse problems and trace class operators
- 2012
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In: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 53:12
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Journal article (peer-reviewed)abstract
- This paper provides a mathematical framework for Fisher information analysis forinverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class, andthe Jacobian of the forward operator Hilbert-Schmidt. We show that the appropriatespace for defining the Fisher information is given by the Cameron-Martin space. This is mainly because the range space of the covariance operator always is strictlysmaller than the Hilbert space. For the Fisher information to be well-defined, it is furthermore required that the range space of the Jacobian is contained in the Cameron-Martin space. In order for this condition to hold and for the Fisher information tobe trace class, a sufficient condition is formulated based on the singular values ofthe Jacobian as well as of the eigenvalues of the covariance operator, together withsome regularity assumptions regarding their relative rate of convergence. An explicit example is given regarding an electromagnetic inverse source problem with “external”spherically isotropic noise, as well as “internal” additive uncorrelated noise.
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| 14. |
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| 15. |
- Nordebo, Sven, et al.
(author)
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Low-frequency dispersion characteristics of a multilayered coaxial cable
- 2013
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In: Journal of Engineering Mathematics. - : Springer Netherlands. - 0022-0833 .- 1573-2703. ; 83:1, s. 169-184
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Journal article (peer-reviewed)abstract
- This paper provides an exact asymptotic analysis regarding the low-frequency dispersion characteristics of a multilayered coaxial cable. A layer-recursive description of the dispersion function is derived that is well suited for asymptotic analysis. The recursion is based on two well-behaved (meromorphic) subdeterminants defined by a perfectly electrically conducting (PEC) and a perfectly magnetically conducting termination, respectively. For an open waveguide structure, the dispersion function is a combination of two such functions, and there is only one branch point that is related to the exterior domain. It is shown that if there is one isolating layer and a PEC outer shield, then the classical Weierstrass preparation theorem can be used to prove that the low-frequency behavior of the propagation constant is governed by the square root of the complex frequency, and an exact analytical expression for the dominating term of the asymptotic expansion is derived. It is furthermore shown that the same asymptotic expansion is valid to its lowest order even if the outer shield has finite conductivity and there is an infinite exterior region with finite nonzero conductivity. As a practical application of the theory, a high-voltage direct current (HVDC) power cable is analyzed and a numerical solution to the dispersion relation is validated by comparisons with the asymptotic analysis. The comparison reveals that the low-frequency dispersion characteristics of the power cable is very complicated and a first-order asymptotic approximation is valid only at extremely low frequencies (below 1 Hz). It is noted that the only way to come to this conclusion is to actually perform the asymptotic analysis. Hence, for practical modeling purposes, such as with fault localization, an accurate numerical solution to the dispersion relation is necessary and the asymptotic analysis is useful as a validation tool.
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| 16. |
- Nordebo, Sven, et al.
(author)
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On the relation between optimal wideband matching and scattering of spherical waves
- 2011
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In: IEEE Transactions on Antennas and Propagation. - 0018-926X .- 1558-2221. ; 59:9, s. 3358-3369
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Journal article (peer-reviewed)abstract
- Abstract in UndeterminedUsing an exact circuit analogy for the scattering ofvector spherical waves, it is shown how the problem of determiningthe optimal scattering bounds for a homogeneous spherein its high-contrast limit is identical to the closely related, andyet very different problem of finding the broadband tuning limitsof the spherical waves. Using integral relations similar to Fano’sbroadband matching bounds, the optimal scattering limitationsare determined by the static response as well as the high-frequencyasymptotics of the reflection coefficient. The scattering view of thematching problem yields explicitly the necessary low-frequencyasymptotics of the reflection coefficient that is used with Fano’sbroadband matching bounds for spherical waves, something thatappears to be non-trivial to derive from the classical networkpoint of view.
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| 17. |
- Nordebo, Sven, et al.
(author)
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Optimal Realizations of Passive Structures
- 2014
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In: IEEE Transactions on Antennas and Propagation. - 0018-926X .- 1558-2221. ; 62:9, s. 4686-4694
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Journal article (peer-reviewed)abstract
- This paper presents a convex optimization approach to study optimal realizations of passive electromagnetic structures. The optimization approach complements recently developed theory and techniques to derive sum rules and physical limitations for passive systems operating over a given bandwidth. The sum rules are based solely on the analytical properties of the corresponding Herglotz functions. However, the application of sum rules is limited by certain assumptions regarding the low- and high-frequency asymptotic behavior of the system, and the sum rules typically do not give much information towards an optimal realization of the passive system at hand. In contrast, the corresponding convex optimization problem is formulated to explicitly generate a Herglotz function as an optimal realization of the passive structure. The procedure does not require any additional assumptions on the low- and high frequency asymptotic behavior, but additional convex constraints can straightforwardly be incorporated in the formulation. Typical application areas are concerned with antennas, periodic structures, material responses, scattering, absorption, reflection, and extinction. In this paper, we consider three concrete examples regarding dispersion compensation for waveguides, passive metamaterials and passive radar absorbers.
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| 18. |
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| 19. |
- Nordebo, Sven, et al.
(author)
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Wave modeling and fault localization for underwater power cables
- 2011
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In: 2011 IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC). - : IEEE Press. - 9781457700460 ; , s. 698-701
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Conference paper (peer-reviewed)abstract
- This paper describes some preliminary results regarding Time-Domain pulse Reflection (TDR) measurements and modeling performed on the Baltic Cable submarine HVDC link between southern Sweden and northern Germany. The measurements were conducted in collaboration between the Linnaeus University, Lund University, Baltic Cable AB and ABB High Voltage Cables AB, and is part of the research project: “Fundamental wave modeling for signal estimation on lossy transmission lines”. Preliminary results on measurements and modeling are included here, as well as a first numerical study regarding the low-frequency dispersion characteristics of power cables. The numerical study shows that the finite conductivity of the cable lead shield has a great impact on the losses at low frequencies (0-1 kHz), and that the low-frequency asymptotics of the propagation constant is consistent with common propagation models based on the skin-effect.
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| 20. |
- Proto, Monica, et al.
(author)
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Transport Infrastructure Surveillance and Monitoring by Electromagnetic Sensing : The ISTIMES Project
- 2010
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In: Sensors. - : MDPI AG. - 1424-8220. ; 10:12, s. 10620-10639
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Journal article (peer-reviewed)abstract
- The ISTIMES project, funded by the European Commission in the frame of a joint Call "ICT and Security" of the Seventh Framework Programme, is presented and preliminary research results are discussed. The main objective of the ISTIMES project is to design, assess and promote an Information and Communication Technologies (ICT)-based system, exploiting distributed and local sensors, for non-destructive electromagnetic monitoring of critical transport infrastructures. The integration of electromagnetic technologies with new ICT information and telecommunications systems enables remotely controlled monitoring and surveillance and real time data imaging of the critical transport infrastructures. The project exploits different non-invasive imaging technologies based on electromagnetic sensing (optic fiber sensors, Synthetic Aperture Radar satellite platform based, hyperspectral spectroscopy, Infrared thermography, Ground Penetrating Radar-, low-frequency geophysical techniques, Ground based systems for displacement monitoring). In this paper, we show the preliminary results arising from the GPR and infrared thermographic measurements carried out on the Musmeci bridge in Potenza, located in a highly seismic area of the Apennine chain (Southern Italy) and representing one of the test beds of the project.
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