Enhanced electrical impedance tomography via the Mumford–Shah functional

Luca Rondi; Fadil Santosa

ESAIM: Control, Optimisation and Calculus of Variations (2001)

  • Volume: 6, page 517-538
  • ISSN: 1292-8119

Abstract

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We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several numerical examples. Our results indicate that this is an effective approach for overcoming the illposedness. Moreover, it has the capability of enhancing the reconstruction while at the same time segmenting the conductivity image.

How to cite

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Rondi, Luca, and Santosa, Fadil. "Enhanced electrical impedance tomography via the Mumford–Shah functional." ESAIM: Control, Optimisation and Calculus of Variations 6 (2001): 517-538. <http://eudml.org/doc/90606>.

@article{Rondi2001,
abstract = {We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several numerical examples. Our results indicate that this is an effective approach for overcoming the illposedness. Moreover, it has the capability of enhancing the reconstruction while at the same time segmenting the conductivity image.},
author = {Rondi, Luca, Santosa, Fadil},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {electrical impedance tomography; inverse problems for elliptic equations; regularization of illposed problem; image enhancement; regularization},
language = {eng},
pages = {517-538},
publisher = {EDP-Sciences},
title = {Enhanced electrical impedance tomography via the Mumford–Shah functional},
url = {http://eudml.org/doc/90606},
volume = {6},
year = {2001},
}

TY - JOUR
AU - Rondi, Luca
AU - Santosa, Fadil
TI - Enhanced electrical impedance tomography via the Mumford–Shah functional
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2001
PB - EDP-Sciences
VL - 6
SP - 517
EP - 538
AB - We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several numerical examples. Our results indicate that this is an effective approach for overcoming the illposedness. Moreover, it has the capability of enhancing the reconstruction while at the same time segmenting the conductivity image.
LA - eng
KW - electrical impedance tomography; inverse problems for elliptic equations; regularization of illposed problem; image enhancement; regularization
UR - http://eudml.org/doc/90606
ER -

References

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