# Enhanced electrical impedance tomography via the Mumford–Shah functional

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

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

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topRondi, 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 -

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