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
  • [11] Algorithm for solving the Electrical Impedance Tomography forward problem by the modification method
    Sushko, I. O.
    VISNYK NTUU KPI SERIIA-RADIOTEKHNIKA RADIOAPARATOBUDUVANNIA, 2011, (47): : 165 - 175
  • [12] Electrical impedance tomography problem with inaccurately known boundary and contact impedances
    Kolehmainen, Ville
    Lassas, Matti
    Ola, Petri
    IEEE TRANSACTIONS ON MEDICAL IMAGING, 2008, 27 (10) : 1404 - 1414
  • [13] hp-Finite element discretisation of the electrical impedance tomography problem
    Ledger, P. D.
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 225 : 154 - 176
  • [14] Numerical Resolution of the Electrical Impedance Tomography Inverse Problem with Fixed Inclusions
    Velasco, Arrianne Crystal
    Darbas, Marion
    Mendoza, Renier
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2021, 16 (03) : 1063 - 1076
  • [15] Using Genetic Algorithm for Electrode Movement Problem in Electrical Impedance Tomography
    Li, Xuefei
    Luo, Ciyong
    Wang, Ping
    Chen, Minyou
    He, Wei
    2008 WORLD AUTOMATION CONGRESS PROCEEDINGS, VOLS 1-3, 2008, : 1804 - +
  • [16] Chest electrical impedance tomography
    Grigoriadis, K.
    Armaganidis, A.
    ARCHIVES OF HELLENIC MEDICINE, 2019, 36 (05): : 589 - 596
  • [17] Rotational electrical impedance tomography
    Huang, Cheng-Ning
    Yu, Fang-Ming
    Chung, Hung-Yuan
    MEASUREMENT SCIENCE AND TECHNOLOGY, 2007, 18 (09) : 2958 - 2966
  • [18] THE SENSITIVITY IN ELECTRICAL IMPEDANCE TOMOGRAPHY
    Rybin, A. I.
    Gaydayenko, E. V.
    Sushko, I. O.
    Gamanenko, A. I.
    VISNYK NTUU KPI SERIIA-RADIOTEKHNIKA RADIOAPARATOBUDUVANNIA, 2013, (55): : 107 - 117
  • [19] FEATURES OF SOLVING THE ELECTRICAL IMPEDANCE TOMOGRAPHY INVERSE PROBLEM BY ZONES CONDUCTIVITIES METHOD
    Sushko, I.
    Rybin, O.
    VISNYK NTUU KPI SERIIA-RADIOTEKHNIKA RADIOAPARATOBUDUVANNIA, 2012, (51): : 106 - 114
  • [20] Evaluation of three different approximations for the solution of the direct problem on electrical impedance tomography
    Martins, J. Santana
    Moura, C. Stein
    Vargas, R. M. Figueiro
    REVISTA INTERNACIONAL DE METODOS NUMERICOS PARA CALCULO Y DISENO EN INGENIERIA, 2015, 31 (01): : 42 - 49
12345