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

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.

3 Pages, 7 Figures

References in corpus (3)

• Convexification of Restricted Dirichlet-to-Neumann Map
• A new version of the convexification method for a 1-D coefficient inverse problem with experimental data
• Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction

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• Discretization and Convergence of the EIT Optimal Control Problem in 2D and 3D Domains