Enhanced electrical impedance tomography via the mumford-shah functional

Luca Rondi, Fadil Santosa

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


We consider the problem of electrical impedance tomography where conductivity distri-bution 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.

Original languageEnglish (US)
Pages (from-to)517-538
Number of pages22
JournalESAIM - Control, Optimisation and Calculus of Variations
StatePublished - Jul 2001


  • Electrical impedance tomography
  • Image enhancement
  • Inverse problems for elliptic equations
  • Regularization of illposed problem


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