The geometrical problem of electrical impedance tomography in the disk

被引：0
|
作者：
Sharafutdinov, V. A. [1 ,2 ]
机构：
[1] Sobolev Inst Math, Novosibirsk, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2011年 / 52卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
electrical impedance tomography; Dirichlet-to-Neumann operator; conformal map; BOUNDARY; MANIFOLDS;
D O I：
10.1134/S0037446606010198
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：178 / 190
页数：13
相关论文
共 50 条
  • [1] The geometrical problem of electrical impedance tomography in the disk
    V. A. Sharafutdinov
    Siberian Mathematical Journal, 2011, 52 : 178 - 190
  • [2] Electrical impedance tomography and Calderon's problem
    Uhlmann, G.
    INVERSE PROBLEMS, 2009, 25 (12)
  • [3] FINITE VOLUME SCHEMES FOR THE ELECTRICAL IMPEDANCE TOMOGRAPHY PROBLEM
    Sherina, E. S.
    Starchenko, A., V
    VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS, 2014, (29): : 25 - 38
  • [4] The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
    Alberti, Giovanni S.
    Ammari, Habib
    Jin, Bangti
    Seo, Jin-Keun
    Zhang, Wenlong
    SIAM JOURNAL ON IMAGING SCIENCES, 2016, 9 (04): : 1525 - 1551
  • [5] ON A CALDERON PROBLEM IN FREQUENCY DIFFERENTIAL ELECTRICAL IMPEDANCE TOMOGRAPHY
    Kim, Sungwhan
    Tamasan, Alexandru
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (05) : 2700 - 2709
  • [6] A New Algorithm for Electrical Impedance Tomography Inverse Problem
    Kriz, T.
    Dedkova, J.
    PIERS 2009 BEIJING: PROGESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, PROCEEDINGS I AND II, 2009, : 127 - 131
  • [7] An analytic simplification for the reconstruction problem of electrical impedance tomography
    Belward, C
    Howes, T
    Forbes, LK
    INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, 2002, 12 (01) : 9 - 15
  • [8] Approximation of the inverse electrical impedance tomography problem by an inverse transmission problem
    Hofmann, B
    INVERSE PROBLEMS, 1998, 14 (05) : 1171 - 1187
  • [9] Recursive estimation of fast impedance changes in electrical impedance tomography and a related problem
    Kaipio, JP
    Somersalo, E
    Karjalainen, PA
    Vauhkonen, M
    COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS, 1997, 3171 : 208 - 216
  • [10] The use of electrical impedance tomography with the inverse problem of EEG and MEG
    Gonçalves, S
    de Munck, JC
    PROCEEDINGS OF THE 22ND ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-4, 2000, 22 : 2346 - 2349
12345