Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps

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Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps. / Hyvönen, Nuutti; Päivärinta, Lassi; Tamminen, Janne.

In: Inverse Problems and Imaging, Vol. 12, No. 2, 03.2018, p. 373-400.

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@article{9aec02d4e699419f921d41cb62ebaf41,
title = "Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps",
abstract = "We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of interest to the unit disk where the D-bar method can be implemented most efficiently. In particular, this applies to the open upper half-plane. Second, in the unit disk we may choose a region of interest that is magnified using a suitable M{\"o}bius transform. To facilitate the efficient use of conformal maps, we introduce input current patterns that are named conformally transformed truncated Fourier basis; in practice, their use corresponds to positioning the available electrodes close to the region of interest. These ideas are numerically tested using simulated continuum data in bounded domains and simulated point electrode data in the half-plane. The connections to practical electrode measurements are also discussed.",
keywords = "Calder{\'o}n problem, D-bar method, conformal mapping, region of interest, half-plane, point electrodes",
author = "Nuutti Hyv{\"o}nen and Lassi P{\"a}iv{\"a}rinta and Janne Tamminen",
year = "2018",
month = "3",
doi = "10.3934/ipi.2018017",
language = "English",
volume = "12",
pages = "373--400",
journal = "Inverse Problems and Imaging",
issn = "1930-8337",
publisher = "AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES",
number = "2",

}

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TY - JOUR

T1 - Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps

AU - Hyvönen, Nuutti

AU - Päivärinta, Lassi

AU - Tamminen, Janne

PY - 2018/3

Y1 - 2018/3

N2 - We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of interest to the unit disk where the D-bar method can be implemented most efficiently. In particular, this applies to the open upper half-plane. Second, in the unit disk we may choose a region of interest that is magnified using a suitable Möbius transform. To facilitate the efficient use of conformal maps, we introduce input current patterns that are named conformally transformed truncated Fourier basis; in practice, their use corresponds to positioning the available electrodes close to the region of interest. These ideas are numerically tested using simulated continuum data in bounded domains and simulated point electrode data in the half-plane. The connections to practical electrode measurements are also discussed.

AB - We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of interest to the unit disk where the D-bar method can be implemented most efficiently. In particular, this applies to the open upper half-plane. Second, in the unit disk we may choose a region of interest that is magnified using a suitable Möbius transform. To facilitate the efficient use of conformal maps, we introduce input current patterns that are named conformally transformed truncated Fourier basis; in practice, their use corresponds to positioning the available electrodes close to the region of interest. These ideas are numerically tested using simulated continuum data in bounded domains and simulated point electrode data in the half-plane. The connections to practical electrode measurements are also discussed.

KW - Calderón problem

KW - D-bar method

KW - conformal mapping

KW - region of interest

KW - half-plane

KW - point electrodes

U2 - 10.3934/ipi.2018017

DO - 10.3934/ipi.2018017

M3 - Article

VL - 12

SP - 373

EP - 400

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 2

ER -

ID: 18045761