The geometrical problem of electrical impedance tomography in the disk |
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Authors: | V. A. Sharafutdinov |
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Affiliation: | (1) IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Sachsen, Germany |
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Abstract: | The geometrical problem of electrical impedance tomography consists of recovering a Riemannian metric on a compact manifold with boundary from the Dirichlet-to-Neumann operator (DNoperator) given on the boundary. We present a new elementary proof of the uniqueness theorem: A Riemannian metric on the two-dimensional disk is determined by its DN-operator uniquely up to a conformal equivalence. We also prove an existence theorem that describes all operators on the circle that are DN-operators of Riemannian metrics on the disk. |
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