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arXiv · 1803.11193

Electrical Impedance Tomography with Restricted Dirichlet-to-Neumann Map Data

Michael V. Klibanov·Jingzhi Li·Wenlong Zhang
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Abstract

We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT) model. "Restricted Dirichlet-to-Neumann (DtN) map data" means that the Dirichlet and Neumann boundary data for EIT are generated by a point source running either along an interval of a straight line or along a curve located outside of the domain of interest. We "convexify" the problem via constructing a globally strictly convex Tikhonov-like functional using a Carleman Weight Function. In particular, two new Carleman estimates are established. Global convergenceto the correct solution of the gradient projection method for this functional is proven. Numerical examples demonstrate a good performance of this numerical procedure.

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Michael V. Klibanov, Jingzhi Li, Wenlong Zhang. 2018-03-29. Electrical Impedance Tomography with Restricted Dirichlet-to-Neumann Map Data. https://doi.org/10.1088/1361-6420%2Faafecd

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