We consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We perform measurements of current and voltage type on a (known) part of the boundary of the conductor. We prove that, even if the defects are unknown, the current and voltage measurements at the boundary uniquely determine the corresponding electrostatic potential inside the conductor. A corresponding stability result, related to the stability of Neumann problems with...

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...

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...

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