Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data. (4th February 2019)

• Record Type: Journal Article
• Authors: Klibanov, Michael V; Li, Jingzhi; Zhang, Wenlong
• Is Part Of: Inverse problems. Volume 35:Number 3(2019)
• Publication Date: 2019-02-04
• Subjects: inverse problem -- Carleman weight function -- global strict convexity -- global convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aafecd
• Languages: English
• ISSNs: 0266-5611

Abstract

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). '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 convergence to the correct solution of the gradient projection method for this functional is proven. Numerical examples demonstrate a good performance of this numerical procedure.