The Inverse Conductivity Problem with an Imperfectly Known Boundary

Kolehmainen, Ville; Lassas, Matti; Ola, Petri

doi:10.1137/040612737

Cited by 73 publications

(85 citation statements)

References 17 publications

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“…These two regions appear as one in these images, although other reconstruction algorithms have resolved two lungs under similar test conditions, as did the D-bar algorithm on the experimental tank data in Isaacson et al 2004. The probable cause for this distortion is modeling the chest by a disc. It is well known that such an approximation can cause artifacts; see Adler et al 1996, Gersing et al 1996, Kolehmainen et al 1997, Kolehmainen et al 2005 …”

Section: Resultsmentioning

confidence: 99%

Imaging cardiac activity by the D-bar method for electrical impedance tomography

et al. 2006

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A practical D-bar algorithm for reconstructing conductivity changes from EIT data taken on electrodes in a 2D geometry is described. The algorithm is based on the global uniqueness proof of Nachman (1996 Ann. Math. 143 71-96) for the 2D inverse conductivity problem. Results are shown for reconstructions from data collected on electrodes placed around the circumference of a human chest to reconstruct a 2D cross-section of the torso. The images show changes in conductivity during a cardiac cycle.

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Section: Resultsmentioning

confidence: 99%

Imaging cardiac activity by the D-bar method for electrical impedance tomography

et al. 2006

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“…Inverse transport see [14] for applications of 60 solutions to inverse problem for the transport equation. The case where the electrical measurements are made on an unknown boundary was considered in [111].…”

Section: Other Applicationsmentioning

confidence: 99%

Inverse problems: seeing the unseen

2014

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This survey article deals mainly with two inverse problems and the relation between them. The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography and also Calderón's problem since the famous analyst proposed it in the mathematical literature (Calderón in On an inverse boundary value problem. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980), Soc Brasil Mat. Rio de Janeiro, pp. [65][66][67][68][69][70][71][72][73] 1980). The second is on travel time tomography. The question is whether one can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as a geometry problem, the boundary rigidity problem. Can we determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points? These two inverse problems concern visibility, that is whether we can determine the internal properties of a medium by making measurements at the boundary. The last topic of this paper considers the opposite issue: invisibility: Can one make objects invisible to different types of waves, including light?Communicated by Ari Laptev.

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“…This type of shape correction could also be interpreted as a type of model reduction error, using the framework developed by Kolehmainen et al to address inexact knowledge of the boundary shape [8], [9]. The relationship between an exact and geometrically inexact domain is modelled [8], [10] (which was extended to contact impedance errors [11]) and, once first-and second-order statistics are computed, combined into the inverse formulation.…”

Section: Introductionmentioning

confidence: 99%

“…The relationship between an exact and geometrically inexact domain is modelled [8], [10] (which was extended to contact impedance errors [11]) and, once first-and second-order statistics are computed, combined into the inverse formulation. This results in the addition of a dense model error matrix to the reconstruction error term.…”

Section: Introductionmentioning

confidence: 99%

Shape Deformation in Two-Dimensional Electrical Impedance Tomography

Boyle

Adler

Lionheart

2012

IEEE Trans. Med. Imaging

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Abstract-Electrical Impedance Tomography (EIT) uses measurements from surface electrodes to reconstruct an image of the conductivity of the contained medium. However, changes in measurements result from both changes in internal conductivity and changes in the shape of the medium relative to the electrode positions. Failure to account for shape changes results in a conductivity image with significant artifacts. Previous work to address shape changes in EIT has shown that in some cases boundary shape and electrode location can be uniquely determined for isotropic conductivities; however, for geometrically conformal changes, this is not possible. This prior work has shown that the shape change problem can be partially addressed. In this paper, we explore the limits of compensation for boundary movement in EIT, using three approaches: first, a theoretical model was developed to separate a deformation vector field into conformal and non-conformal components, from which the reconstruction limits may be determined; next, finite element models were used to simulate EIT measurements from a domain whose boundary has been deformed; finally, an experimental phantom was constructed from which boundary deformation measurements were acquired. Results, both in simulation and with experimental data, suggest that some electrode movement and boundary distortions can be reconstructed based on conductivity changes alone while reducing image artifacts in the process.

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The Inverse Conductivity Problem with an Imperfectly Known Boundary

Cited by 73 publications

References 17 publications

Imaging cardiac activity by the D-bar method for electrical impedance tomography

Imaging cardiac activity by the D-bar method for electrical impedance tomography

Inverse problems: seeing the unseen

Shape Deformation in Two-Dimensional Electrical Impedance Tomography

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