| 11. |
- Ludvig-Osipov, Andrei, et al.
(författare)
-
Fundamental Bounds on Transmission Through Periodically Perforated Metal Screens With Experimental Validation
- 2020
-
Ingår i: IEEE Transactions on Antennas and Propagation. - : IEEE. - 0018-926X .- 1558-2221. ; 68:2, s. 773-782
-
Tidskriftsartikel (refereegranskat)abstract
- This article presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil.
|
|
| 12. |
- Nordebo, Sven, et al.
(författare)
-
A Green's function approach to Fisher information analysis and preconditioning in microwave tomography
- 2010
-
Ingår i: Inverse Problems in Science and Engineering. - : Informa UK Limited. - 1741-5977 .- 1741-5985. ; 18:8, s. 1043-1063
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 13. |
- Nordebo, Sven, 1963-, et al.
(författare)
-
A priori modeling for gradient based inverse scattering algorithms
- 2009
-
Ingår i: Progress in Electromagnetics Research B. - 1937-6472. ; 16, s. 407-432
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a Fisher information based Bayesian approach to analysis and design of the regularization and preconditioning parameters used with gradient based inverse scattering algorithms. In particular, a one-dimensional inverse problem is considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A priori parameter modeling is considered with linear, exponential and arctangential parameter scalings and robust preconditioners are obtained by choosing the related scaling parameters based on a Fisher information analysis of the known background. The Bayesian approach and a principal parameter (singular value) analysis of the stochastic Cramer-Rao bound provide a natural interpretation of the regularization that is necessary to achieve stable inversion, as well as an indicator to predict the feasibility of achieving successful reconstruction in a given problem set-up. In particular, the Tikhonov regularization scheme is put into a Bayesian estimation framework. A time-domain least-squares inversion algorithm is employed which is based on a quasi-Newton algorithm together with an FDTD-electromagnetic solver. Numerical examples are included to illustrate and verify the analysis.
|
|
| 14. |
- Nordebo, Sven, et al.
(författare)
-
A Systematic Approach to Robust Preconditioning for Gradient Based Inverse Scattering Algorithms
- 2008
-
Ingår i: Inverse Problems. - : IOP Publishing. - 1361-6420 .- 0266-5611. ; 24:2, s. 025027-
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient or quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit diagonal. By improving the conditioning of the Hessian, the convergence rate of the conjugate gradient or quasi-Newton methods are improved. The preconditioner is robust in the sense that the scaling, i.e. the diagonal Fisher information, is virtually invariant to the numerical resolution and the discretization model that is employed. Numerical examples of image reconstruction are included to illustrate the efficiency of the proposed technique. © 2008 IOP Publishing Ltd.
|
|
| 15. |
- Nordebo, Sven, et al.
(författare)
-
An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography
- 2010
-
Ingår i: Inverse Problems. - : IOP Publishing. - 1361-6420 .- 0266-5611. ; 26:12
-
Tidskriftsartikel (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 compatible 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.
|
|
| 16. |
|
|
| 17. |
|
|
| 18. |
- Nordebo, Sven, et al.
(författare)
-
Cylindrical multipole expansion for periodic sources with applications for three-phase power cables
- 2018
-
Ingår i: Mathematical methods in the applied sciences. - : Wiley-Blackwell. - 0170-4214 .- 1099-1476. ; 41:3, s. 959-965
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a c ylindrical multipole expansion for periodic sources with applications for three-phase power cables.It is the aim of the contribution to provide some analytical solutions and techniques that can be useful in the calculation ofcable losses. Explicit analytical results are given for the fields generated by a three-phase helical current distribution andwhich can be computed efficiently as an input to other numerical methods such as, for example , the Method of Moments.It is shown that the field computations are numerically stable at low frequencies (such as 50 Hz) as well as in the quasi-magnetostatic limit provided that sources are divergence-free. The cylindrical multipole expansion is fur thermore usedto derive an efficient analytical model of a measurement coil to measure and estimate the complex valued permeability ofmagnetic steel armour in the presence of a strong skin-effect.
|
|
| 19. |
- Nordebo, Sven, et al.
(författare)
-
Data fusion for electromagnetic and electrical resistive tomography based on maximum likelihood
- 2011
-
Ingår i: International Journal of Geophysics. - : Hindawi Limited. - 1687-885X .- 1687-8868. ; 2011
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a maximum likelihood based approach to data fusion for electromagnetic (EM) and electrical resistive (ER) tomography. The statistical maximum likelihood criterion is closely linked to the additive Fisher information measure, and it facilitates an appropriate weighting of the measurement data which can be useful with multiphysics inverse problems. The Fisher information is particularly useful for inverse problems which can be linearized similar to the Born approximation. In this paper, a proper scalar product is defined for the measurements and a truncated Singular Value Decomposition (SVD) based algorithm is devised which combines the measurement data of the two imaging modalities in a way that is optimal in the sense of maximum likelihood. As a multiphysics problem formulation with applications in geophysics, the problem of tunnel detection based on EM and ER tomography is studied in this paper. To illustrate the connection between the Green's functions, the gradients and the Fisher information, two simple and generic forward models are described in detail regarding two-dimensional EM and ER tomography, respectively.
|
|
| 20. |
|
|
