| 21. |
- Nordebo, Sven, et al.
(författare)
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Data fusion for reconstruction algorithms via different sensors in geophysical sensing
- 2011
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Ingår i: Journal of Geophysics and Engineering. - 1742-2140 .- 1742-2132. ; 8:3, s. 54-60
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Tidskriftsartikel (refereegranskat)abstract
- Abstract in UndeterminedInformation fusion via multimodal inverse problems and different sensors is addressed using a Fisher information analysis approach. The Fisher information measure is inherently additive, and it facilitates an appropriate weighting of the measurement data that is statistically optimal and can hence be useful with reconstruction algorithms in geophysical sensing. Given that there exists proper knowledge about the sensor noise statistics, correlations and spectral contents, as well as a correct forward model, the Fisher information is a natural measure of information because it is closely linked to the statistical maximum likelihood principle. To illustrate the concept of data correlation based on statistical Fisher information analysis, two simple and generic examples are employed in electrical resistivity and electromagnetic tomography, which are motivated by geophysical applications, such as tunnel detection. The examples demonstrate that a properly weighted data fusion can be of crucial importance for an ill-posed multimodal inverse problem.
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| 22. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis and preconditioning in electrical impedance tomography
- 2010
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Ingår i: Journal of Physics: Conference Series 224 (2010), 1742-6588. - : IOP Publishing. - 1742-6596 .- 1742-6588. ; , s. 012057-
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Konferensbidrag (refereegranskat)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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| 23. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis in electrical impedance tomography
- 2013
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Ingår i: Journal of Geophysics and Engineering. - : Institute of Physics (IOP). - 1742-2132 .- 1742-2140. ; 10:6, s. Article ID: 064008-
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Tidskriftsartikel (refereegranskat)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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| 24. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis in microwave tomography
- 2009
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Ingår i: The Third International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP09). - 9781424451807 ; , s. 217-220
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Konferensbidrag (refereegranskat)
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| 25. |
- Nordebo, Sven, et al.
(författare)
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Fisher information for inverse problems and trace class operators
- 2012
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 53:12
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Tidskriftsartikel (refereegranskat)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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| 26. |
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| 27. |
- Nordebo, Sven, et al.
(författare)
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Low-frequency dispersion characteristics of a multilayered coaxial cable
- 2013
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Ingår i: Journal of Engineering Mathematics. - : Springer Netherlands. - 0022-0833 .- 1573-2703. ; 83:1, s. 169-184
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Tidskriftsartikel (refereegranskat)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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| 28. |
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| 29. |
- Nordebo, Sven, et al.
(författare)
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On the Design of Optimal Measurements for Antenna Near-Field Imaging Problems
- 2006
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Ingår i: AIP Conference Proceedings. - : AIP. ; 834, s. 234-249
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Konferensbidrag (refereegranskat)abstract
- A mathematical framework is introduced for optimization of antenna near-field imaging problems, based on the multipole expansion of the electromagnetic field, the Fisher information to quantify the quality of data and use of modern interior point convex optimization techniques. We consider the general problem of optimizing the measurement sensor allocation for parameter estimation in distributed systems, and in particular the problem of optimizing the measurement set-up for antenna near-field estimation. As an application example for antenna near-field imaging, we consider a relevant measurement set-up using cylindrical probing coordinates. The convex optimization problem is examined using duality theory, and it is shown that several structural properties of the optimal measurement problem can be exploited in developing an efficient interior point optimization method. In particular, we show that the cylindrical measurement set-up yields a Fisher information matrix with block diagonal structure, a feature which can be directly exploited in the optimization algorithm by reducing the number of dual decision variables.
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| 30. |
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