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Sökning: LAR1:lu > Gustafsson Mats > Chalmers tekniska högskola > Linnéuniversitetet

  • Resultat 1-7 av 7
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  • Fhager, Andreas, et al. (författare)
  • Image Reconstruction in Microwave Tomography Using a Dielectric Debye Model
  • 2012
  • Ingår i: IEEE Transactions on Biomedical Engineering. - 0018-9294. ; 59:1, s. 156-166
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, quantitative dielectric image reconstruction based on broadband microwave measurements is investigated. A time-domain-based algorithm is derived where Debye model parameters are reconstructed in order to take into account the strong dispersive behavior found in biological tissue. The algorithm is tested with experimental and numerical data in order to verify the algorithm and to investigate improvements in the reconstructed image resulting from the improved description of the dielectric properties of the tissue when using broadband data. The comparison is made in relation to the more commonly used conductivity model. For the evaluation, two examples were considered, the first was a lossy saline solution and the second was less lossy tap water. Both liquids are strongly dispersive and used as a background medium in the imaging examples. The results show that the Debye model algorithm is of most importance in the tap water for a bandwidth of more than 1.5 GHz. Also the saline solution exhibits a dispersive behavior but since the losses restrict the useful bandwidth, the Debye model is of less significance even if somewhat larger and stronger artifacts can be seen in the conductivity model reconstructions
  • 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. - Taylor & Francis. - 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 Cram<img src="http://www.informaworld.com/cache/entities/14/000000/ffffff/arial/md/00e9.png" />r-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.
  • Nordebo, Sven, et al. (författare)
  • A Systematic Approach to Robust Preconditioning for Gradient Based Inverse Scattering Algorithms
  • 2008
  • Ingår i: Inverse Problems. - 0266-5611. ; 24:2
  • 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.
  • Nordebo, Sven, et al. (författare)
  • An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography
  • 2010
  • Ingår i: Inverse Problems. - 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.
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