Numer. Math. (2018) 138:723–765
Identifying conductivity in electrical impedance
tomography with total variation regularization
· Barbara Kaltenbacher
· Tran Nhan Tam Quyen
Received: 20 September 2016 / Revised: 13 July 2017 / Published online: 25 September 2017
© Springer-Verlag GmbH Deutschland 2017
Abstract 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.
Keywords Conductivity identiﬁcation · Electrical impedance tomography · Total
variation regularization · Finite element method · Neumann problem · Dirichlet
problem · Ill-posed problems
Mathematics Subject Classiﬁcation 65N21 · 65N12 · 35J25 · 35R30
M. Hinze gratefully acknowledges support of the Lothar Collatz Center for Computing in Science at the
University of Hamburg.
B. Kaltenbacher gratefully acknowledges support of the Austrian Wissenschaftsfonds through grant FWF
I2271 entitled “Solving inverse problems without forward operators”.
T.N.T. Quyen gratefully acknowledges support of the Alexander von Humboldt-Foundation.
Tran Nhan Tam Quyen
University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt, Austria