Identifying conductivity in electrical impedance tomography with total variation regularization

被引：32

作者：

Hinze, Michael ^{[1
]}

Kaltenbacher, Barbara ^{[2
]}

Tran Nhan Tam Quyen ^{[1
]}

机构：

[1] Univ Hamburg, Bundesstr 55, D-20146 Hamburg, Germany

[2] Alpen Adria Univ Klagenfurt, Univ Str 65-67, A-9020 Klagenfurt, Austria

来源：

NUMERISCHE MATHEMATIK | 2018年 / 138卷 / 03期

关键词：

Conductivity identification; Electrical impedance tomography; Total variation regularization; Finite element method; Neumann problem; Dirichlet problem; Ill-posed problems; BOUNDARY-VALUE PROBLEM; LOCAL REGULARIZATION; COMPUTED-TOMOGRAPHY; GLOBAL UNIQUENESS; INVERSE; APPROXIMATION;

D O I：

10.1007/s00211-017-0920-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the problem of identifying the conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We discretize the PDE as well as the conductivity with piecewise linear, continuous finite elements. We prove the stability and convergence of this technique. For the numerical solution we propose a projected Armijo algorithm. Finally, a numerical experiment is presented to illustrate our theoretical results.

引用

页码：723 / 765

页数：43

共 43 条

[1]

Adams RA., 1975, Sobolev Spaces

[2] LOCAL UNIQUENESS IN THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT [J].