Enhanced Electrical Impedance Tomography via the Mumford–Shah Functional
Institut für Industriemathematik/SFB ,
Johannes Kepler Universität Linz, Austria. :
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
2 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.; firstname.lastname@example.org.
Revised: 12 April 2001
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.
Mathematics Subject Classification: 35R25 / 35R30 / 35J25 / 68U10
Key words: Electrical impedance tomography / inverse problems for elliptic equations / regularization of illposed problem / image enhancement.
© EDP Sciences, SMAI, 2001