Fisher information analysis and preconditioning in electrical impedance tomography

Nordebo, Sven; Bayford, Richard; Bengtsson, Bengt; Fhager, Andreas; Gustafsson, Mats; Hashemzadeh, Parham; Nilsson, Börje; Rylander, Thomas; Sjödén, Therese

doi:10.1088/1742-6596/224/1/012057

Cited by 4 publications

(7 citation statements)

References 6 publications

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“…where δF = δ θ T (r) F δθdV and δ θ(r) Z mnq is given by (27). Note that they are the same impedance gradients δ θ(r) Z mnq given by ( 27) that are used in the calculation of the Fisher information I(r , r ) in ( 26), as well as in the calculation of the total gradient δ θ(r) F in (28).…”

Section: Fisher Information-based Preconditioning For Gradient-based ...mentioning

confidence: 99%

“…In a numerical implementation, the gradients in (27) are replaced by finite gradients with respect to the discrete parameter values θ ij :…”

Section: Fisher Information-based Preconditioning For Gradient-based ...mentioning

confidence: 99%

“…Note that the calculation of the Fisher information ( 26) is based on the same impedance gradients (27) that are used to calculate the gradient of the misfit functional in (28). The parameter model is given by (25) where the known background parameters are β = 80 and r = 80 (the loss tangent of the background is 1.0 at ν = 1) and where the five discrete frequencies The FEM with triangular elements and linear interpolation [19] was used to solve the direct and adjoint problems ( 7) and ( 15), respectively, and the resulting fields were used as an input to calculate the impedance gradients (27). The mesh generator DistMesh [32,33] was used to generate a non-uniform mesh (fine close to the electrodes) of the circular domain.…”

Section: Simulation Study Of Sensitivity Balancementioning

confidence: 99%

“…In [28], the Fisher information operator was furthermore defined in a variational framework that is suitable for the analytical Green's function and gradientbased approaches in microwave tomography. In this contribution, it is shown how the Fisher information can be computed by using the adjoint field techniques, and integrated with the gradient calculations used for optimization in EIT, see also [27]. An in-depth description of the connection between the Fisher information analysis and the singular value decomposition (SVD) of the forward operator is also included.…”

Section: Introductionmentioning

confidence: 99%

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An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography

Nordebo¹,

Bayford²,

Bengtsson³

et al. 2010

Inverse Problems

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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 wellbalanced 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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Section: Fisher Information-based Preconditioning For Gradient-based ...mentioning

confidence: 99%

“…In a numerical implementation, the gradients in (27) are replaced by finite gradients with respect to the discrete parameter values θ ij :…”

Section: Fisher Information-based Preconditioning For Gradient-based ...mentioning

confidence: 99%

Section: Simulation Study Of Sensitivity Balancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography

Nordebo¹,

Bayford²,

Bengtsson³

et al. 2010

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…For applications other than SVO, different information metrics are indeed often used in preconditioning strategies [ 23 ] to improve the convergence properties of quasi-Newton optimizers [ 24 ], to quantify the ill-posedness of the reconstruction [ 25 ], and to explicitly describe the trade-off between accuracy and resolution [ 26 , 27 ].…”

Section: Introductionmentioning

confidence: 99%

Different Metrics for Singular Value Optimization in Near-Field Antenna Characterization

Capozzoli

Curcio

Liseno

2021

Sensors

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We deal with the use of different metrics in the framework of the Singular Value Optimization (SVO) technique for near-field antenna characterization. SVO extracts the maximum amount of information on an electromagnetic field over a certain domain from field samples on an acquisition domain, with a priori information on the source, e.g., support information. It determines the field sample positions by optimizing a functional featuring the singular value dynamics of the radiation operator and representing a measure of the information collected by the field samples. Here, we discuss in detail and compare the use, in the framework of SVO, of different objective functionals and so of different information measures: Shannon number, mutual information, and Fisher information. The numerical results show that they yield a similar performance.

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An image reconstruction algorithm based on Bayesian theorem for electrical resistance tomography

Liu

Han

Zhang

2014

Optik

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Fisher information analysis and preconditioning in electrical impedance tomography

Cited by 4 publications

References 6 publications

An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography

An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography

Different Metrics for Singular Value Optimization in Near-Field Antenna Characterization

An image reconstruction algorithm based on Bayesian theorem for electrical resistance tomography

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