# Enhanced Electrical Impedance Tomography via the Mumford–Shah Functional

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 517-538. <http://eudml.org/doc/116576>.

@article{Rondi2010,

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.; electrical impedance tomography; regularization; image enhancement},

language = {eng},

month = {3},

pages = {517-538},

publisher = {EDP Sciences},

title = {Enhanced Electrical Impedance Tomography via the Mumford–Shah Functional},

url = {http://eudml.org/doc/116576},

volume = {6},

year = {2010},

}

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

DA - 2010/3//

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.; electrical impedance tomography; regularization; image enhancement

UR - http://eudml.org/doc/116576

ER -

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