## Enhanced Electrical Impedance Tomography via the Mumford-Shah Functional (2001)

Venue: | ESAIM: Control, Optimization and Calculus of Variations |

Citations: | 14 - 0 self |

### BibTeX

@ARTICLE{Rondi01enhancedelectrical,

author = {Luca Rondi and Fadil Santosa},

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

journal = {ESAIM: Control, Optimization and Calculus of Variations},

year = {2001},

volume = {6},

pages = {517--538}

}

### OpenURL

### 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 MumfordShah 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 eective approach for overcoming the illposedness. Moreover, it has the capability of enhancing the reconstruction while at the same time segmenting the conductivity image. 1 Introduction and formulation of the problem The purpose of this work is to demonstrate that the Mumford-Shah functional from image processing can be used eectively to regularize the classical problem of electrical impedance tomography. In electrical impedance tomogr...

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Citation Context ...later, the work of J. Sylvester and G. Uhlmann [Sy-U], provided the denitive uniqueness results on this problem. For an overview discussion on uniqueness we refer to a recent monograph by V. Isakov, [=-=I-=-]. In this paper we shall deal with the reconstruction issue, that is, we are looking for a procedure which allows us to recover the unknown conductivity from the knowledge, possibly partial, of the ... |

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Citation Context ... at the cost of loss of resolution. In this work, we explore the use of techniques from image processing, which stabilizes and enhances the reconstruction. An earlier work of D. Dobson and F. Santosa =-=[D-S]-=- employed minimal total variation (TV) criterion, which is popular in image processing, to stabilize and enhance the reconstruction for electrical impedance tomography. In the present work, we also bo... |

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Citation Context ...oduces also a minimum for the original functional. Moreover they showed that if (; K) solves the variational problem, then is indeed piecewise C 1 , that is 2 C 1( nK). In a similar framework in [Co=-=-Ta]-=- the existence of a solution has been proved also for the minimal partition problem (1.6). The computational problem associated with these functionals is an active area of research. A main diculty is ... |

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