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1 results

  • Enhanced Electrical ImpedanceTomography via the Mumford–Shah Functional

  • Luca Rondi, Fadil Santosa
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 6 / 2001
    Published online by Cambridge University Press:
    15 August 2002, pp. 517-538
    Print publication:
    2001

  • We consider the problem of electrical impedance tomography where conductivitydistribution in a domain is to be reconstructed from boundary measurements ofvoltage and currents. It is well-known that this problem is highlyillposed. 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 overcomingthe illposedness. Moreover, it has the capability of enhancing thereconstruction while at the same time segmentingthe conductivity image.