Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data

Klibanov, Michael, V1; Li, Jingzhi2; Zhang, Wenlong2

2019-03

10.1088/1361-6420/aafecd

INVERSE PROBLEMS   影响因子和分区

0266-5611

1361-6420

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-Netunann (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.

inverse problem Carleman weight function global strict convexity global convergence

SCI ; EI

英语

通讯

Shenzhen Sci-Tech Fund[JCYJ20160530184212170] ; Shenzhen Sci-Tech Fund[JCYJ20170818153840322]

Mathematics ; Physics

Mathematics, Applied ; Physics, Mathematical

WOS:000457723100001

IOP PUBLISHING LTD

20191706815493

Electric impedance ; Electric impedance measurement ; Electric impedance tomography ; Numerical methods

Electricity: Basic Concepts and Phenomena:701.1 ; Numerical Methods:921.6 ; Electric Variables Measurements:942.2

PHYSICS

Web of Science

1.Univ North Carolina Charlotte, Dept Math & Stat, Charlotte, NC 28223 USA
2.Southern Univ Sci & Technol SUSTech, Dept Math, 1088 Xueyuan Blvd, Shenzhen, Guangdong, Peoples R China

Klibanov, Michael, V,Li, Jingzhi,Zhang, Wenlong. Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data[J]. INVERSE PROBLEMS,2019,35(3).

Klibanov, Michael, V,Li, Jingzhi,&Zhang, Wenlong.(2019).Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data.INVERSE PROBLEMS,35(3).

Klibanov, Michael, V,et al."Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data".INVERSE PROBLEMS 35.3(2019).