Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms. / Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim.

In: Applicable Analysis, Vol. 91, No. 4, 2012, p. 737-755.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Author

Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim / Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms.

In: Applicable Analysis, Vol. 91, No. 4, 2012, p. 737-755.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

Bibtex

@article{0ac80444916548a2889560e3c37c17a4,
title = "Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms",
keywords = "Numerical solution, Calderon problem, Moment method, Hyperinterpolation, Reconstruction algorithm, Electrical Impedance Tomography",
publisher = "Taylor & Francis Ltd.",
author = "Fabrice Delbary and Hansen, {Per Christian} and Kim Knudsen",
year = "2012",
doi = "10.1080/00036811.2011.598863",
volume = "91",
number = "4",
pages = "737--755",
journal = "Applicable Analysis",
issn = "0003-6811",

}

RIS

TY - JOUR

T1 - Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms

A1 - Delbary,Fabrice

A1 - Hansen,Per Christian

A1 - Knudsen,Kim

AU - Delbary,Fabrice

AU - Hansen,Per Christian

AU - Knudsen,Kim

PB - Taylor & Francis Ltd.

PY - 2012

Y1 - 2012

N2 - In three dimensions the Calderon problem was addressed and solved in theory in the 1980s. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conductivity equation and a (non-physical) scattering transform. The resulting reconstruction algorithm is in principle direct and addresses the full non-linear problem immediately. In this paper a new simplication of the algorithm is suggested. The method is based on solving a boundary integral equation for the complex geometrical optics solutions, and the method is implemented numerically using a Nystrom method. Convergence estimates are obtained using hyperinterpolation operators. We compare the method numerically to two other approximations by evaluation on two numerical examples. In addition a moment method for the numerical solution of the forward problem is given.

AB - In three dimensions the Calderon problem was addressed and solved in theory in the 1980s. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conductivity equation and a (non-physical) scattering transform. The resulting reconstruction algorithm is in principle direct and addresses the full non-linear problem immediately. In this paper a new simplication of the algorithm is suggested. The method is based on solving a boundary integral equation for the complex geometrical optics solutions, and the method is implemented numerically using a Nystrom method. Convergence estimates are obtained using hyperinterpolation operators. We compare the method numerically to two other approximations by evaluation on two numerical examples. In addition a moment method for the numerical solution of the forward problem is given.

KW - Numerical solution

KW - Calderon problem

KW - Moment method

KW - Hyperinterpolation

KW - Reconstruction algorithm

KW - Electrical Impedance Tomography

UR - http://www.tandfonline.com/doi/abs/10.1080/00036811.2011.598863

U2 - 10.1080/00036811.2011.598863

DO - 10.1080/00036811.2011.598863

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 4

VL - 91

SP - 737

EP - 755

ER -