Comparing reconstruction methods for electrical impedance tomography

Yorkey, Thomas J.

doi:10.1007/bf02584294

Cited by 34 publications

(69 citation statements)

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“…Moreover, for σ = 1 the last term vanishes leaving an equivalent source function in the form of an electric dipole q(r) ≈ −∇δ(r ) · ∇u(r) of moment |∇u(r)| positioned at r , a result consistent with Yorkey's compensation method in electrical resistor networks [14].…”

Section: Q(r) ≈ −∇δσ(R) · ∇U(r) − δσ(R)∇ · ∇U(r)supporting

confidence: 65%

Linearization Error in Electrical Impedance Tomography

Polydorides¹

2009

PIER

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Abstract-In borehole electromagnetic tomography and resistivity survey a linearized model approximation is often used, in the context of regularized regression, to image the conductivity distribution in a domain of interest.Due to the error introduced by the simplified model, quantitative image reconstruction becomes challenging without implementing a nonlinear algorithm. We derive a closed form expression of the linearization error in electrical impedance tomography based on the complete electrode model. The error term is expressed in an integral form involving the gradient of the perturbed electric potential in the interior of the domain and renders itself readily available for analytical or numerical computation. For real isotropic conductivity inhomogeneities with piecewise uniform characteristic functions the perturbed potential field can be shown to satisfy Poisson's equation with Robin boundary conditions and interior point sources positioned at the interfaces of the inclusions. Simulation experiments using a finite element method have been performed to validate these results.

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Section: Q(r) ≈ −∇δσ(R) · ∇U(r) − δσ(R)∇ · ∇U(r)supporting

confidence: 65%

Linearization Error in Electrical Impedance Tomography

Polydorides¹

2009

PIER

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“…As we are interested in non-homogeneous conductivity distributions on irregular domains Finite Element Method (FEM) is the natural choice [81,11,70,73,74,56,55,52] , although finite difference [54] and finite volume methods [23,84]have also been employed. Where the conductivity is known and homogeneous in some sub domain, especially a neighbourhood of the boundary, and attractive proposition is to use a hybrid boundary element and finite element method [36].…”

Section: Choice Of Methodsmentioning

confidence: 99%

EIT reconstruction algorithms: pitfalls, challenges and recent developments

2004

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Abstract. We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Conference on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or "inverse crimes" to avoid.

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“…Typically the electric field strength is also less away from the boundary. This continuum argument is paralleled in Yorkey's 'compensation' method in resistor networks [164]. A resistor in a network is changed and Yorkey observes that to first order the change in voltage at each point in the network is equivalent to the voltage which would result if a current source were applied in parallel with that resistor.…”

Section: Box 14: Sensitivity To a Localised Change In Conductivitymentioning

confidence: 99%

“…The major algorithms presented here have all been tested on tank data. Yorkey [164] compared Tikhonov regularizied Gauss-Newton with ad hoc algorithms on two dimensional tanks, Goble [63,64] and Metherall [102,101] applied one step regularized Gauss-Newton to 3D tanks. P Vauhkonen [153,156] applied a fully iterative regularized Gauss-Newton method to 3D tank data using the complete electrode model.…”

Section: Practical Applicationsmentioning

confidence: 99%