A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images

Vauhkonen, Marko; Lionheart, William R B; Heikkinen, Lasse; Vauhkonen, P J; Kaipio, Jari P.

doi:10.1088/0967-3334/22/1/314

Cited by 217 publications

(153 citation statements)

References 6 publications

(6 reference statements)

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“…The linearization error was tested using the three-dimensional implementation of the complete electrode model in EIDORS 3D [9], while for the equivalent Poisson's sources we have opted for the twodimensional EIDORS 2D [13] implementation of the model in order to enhance the visualization clarity. The results tabulated in Table 1 show the magnitude of the conductivity change, the change in the boundary voltage measurement corresponding to an arbitrarily chosen pair of current and measurement patterns, the contribution of the linear integral term (29) in the measurement change and the value of the linearization error (30).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…[7] who analyze and compare the model to other more abstract models with emphasis on the profile of the boundary current density, and Pidcock et al [8] who provide some analytic solutions for domains with regular geometries. The model has been implemented numerically and distributed under general public licence by Vauhkonen et al [13] and by Polydorides et al in [9] for two and three-dimensional problems respectively. A comprehensive discussion on the electrical imaging models, as indeed the technology and applications of impedance imaging can be found in the reviews by Borcea [2] and the textbooks by Kaipio et al [6] and Holder [5].…”

Section: Introductionmentioning

confidence: 99%

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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: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…No change to the likelihood in (10) is needed to account for this situation, but a slight modification is needed to the prior in (11), by considering the distribution of the resistivities of the unassigned pixels given the assigned:…”

Section: Bayesian Modellingmentioning

confidence: 99%

“…Tomographic techniques, where a section through an object is imaged using measurements taken outside or on the boundary of the object (see for example Cheney et al Maxwell's equations for ERT and the corresponding boundary conditions (Somersalo et al 1992) for electromagnetism. In practice this is done numerically, here using the finite element method (Vauhkonen et al 2001). This is the direct problem or forward solution.…”

Section: Introductionmentioning

confidence: 99%

Conditional Bayes reconstruction for ERT data using resistance monotonicity information

Aykroyd¹,

Soleimani²,

Lionheart³

2006

Meas. Sci. Technol.

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Abstract. Many applications of tomography seek to image two-phase materials, such as oil and air, with the idealized aim of producing a binary reconstruction. The method of Tamburrino et al. (2002) provides a non-iterative approach, which requires modest computational effort, and hence appears to achieve this aim. Specifically, it requires the solution of a number of forward problems increasing only linearly with the number of elements used to represent the domain where the resistivity is unknown. However, even when low measurement noise is present it may be that not all domain elements can be classified and hence only a partial reconstruction is possible. This paper looks at the use of a Bayesian approach based on the monotonicity information for reconstructing the shape of a homogeneous resistivity inclusion in another homogeneous resistivity material. In particular, the monotonicity criterion is used to fix the resistivity of some pixels. The uncertain pixel resistivities are then estimated, conditional upon the fixed values. This has the effect of both producing better reconstructions, but also reducing the computational burden by up to an order of magnitude in the examples considered. The methods are illustrated using simulation examples covering a range of object geometries.

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A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images

Cited by 217 publications

References 6 publications

Linearization Error in Electrical Impedance Tomography

Linearization Error in Electrical Impedance Tomography

EIT reconstruction algorithms: pitfalls, challenges and recent developments

Conditional Bayes reconstruction for ERT data using resistance monotonicity information

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