An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin; Peter Maass

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 4, page 1027-1048
  • ISSN: 1292-8119

Abstract

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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 Lp-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.

How to cite

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Jin, Bangti, and Maass, Peter. "An analysis of electrical impedance tomography with applications to Tikhonov regularization." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 1027-1048. <http://eudml.org/doc/272908>.

@article{Jin2012,
abstract = {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 Lp-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.},
author = {Jin, Bangti, Maass, Peter},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {electrical impedance tomography; Tikhonov regularization; convergence rate},
language = {eng},
number = {4},
pages = {1027-1048},
publisher = {EDP-Sciences},
title = {An analysis of electrical impedance tomography with applications to Tikhonov regularization},
url = {http://eudml.org/doc/272908},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Jin, Bangti
AU - Maass, Peter
TI - An analysis of electrical impedance tomography with applications to Tikhonov regularization
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2012
PB - EDP-Sciences
VL - 18
IS - 4
SP - 1027
EP - 1048
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 Lp-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.
LA - eng
KW - electrical impedance tomography; Tikhonov regularization; convergence rate
UR - http://eudml.org/doc/272908
ER -

References

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