# An analysis of electrical impedance tomography with applications to Tikhonov regularization

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

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

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topJin, 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 -

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