TY - JOUR
T1 - An analysis of electrical impedance tomography with applications to Tikhonov regularization
AU - Jin, Bangti
AU - Maass, Peter
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors would like to thank two anonymous referees for their constructive comments which have led to an improved presentation of the manuscript. The work of Bangti Jin was substantially supported by the Alexander von Humboldt foundation through a postdoctoral researcher fellowship and is partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and that of Peter Maass by the German Science Foundation through grant MA 1657/18-1.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/1/16
Y1 - 2012/1/16
N2 - This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in L p-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov regularization, for both linearized and nonlinear models. Some important properties, e.g., existence, stability, consistency and convergence rates, are established. This provides some theoretical justifications of their practical usage. © EDP Sciences, SMAI, 2012.
AB - This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in L p-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov regularization, for both linearized and nonlinear models. Some important properties, e.g., existence, stability, consistency and convergence rates, are established. This provides some theoretical justifications of their practical usage. © EDP Sciences, SMAI, 2012.
UR - http://hdl.handle.net/10754/597509
UR - http://www.esaim-cocv.org/10.1051/cocv/2011193
UR - http://www.scopus.com/inward/record.url?scp=84864285214&partnerID=8YFLogxK
U2 - 10.1051/cocv/2011193
DO - 10.1051/cocv/2011193
M3 - Article
SN - 1292-8119
VL - 18
SP - 1027
EP - 1048
JO - ESAIM: Control, Optimisation and Calculus of Variations
JF - ESAIM: Control, Optimisation and Calculus of Variations
IS - 4
ER -