Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

Matthias Gehre; Tobias Kluth; Antti Lipponen; Bangti Jin; Aku Seppänen; Jari P. Kaipio; Peter Maass

doi:10.1016/j.cam.2011.09.035

Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

Matthias Gehre, Tobias Kluth, Antti Lipponen, Bangti Jin, Aku Seppänen, Jari P. Kaipio, Peter Maass

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Abstract

We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ℓ1-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ℓ1-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. © 2011 Elsevier B.V. All rights reserved.

Original language	English (US)
Pages (from-to)	2126-2136
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	236
Issue number	8
DOIs	https://doi.org/10.1016/j.cam.2011.09.035
State	Published - Feb 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The work of BJ was substantially supported by the Alexander von Humboldt Foundation through a postdoctoral researcher fellowship and partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and that of PM was supported by the German Science Foundation through grant MA 1657/18-1. AL, AS and JK were supported by the Academy of Finland (application number 213476, Finnish Programme for Centres of Excellence in Research 2006-2011), TEKES (Contract No. 40370/06), Finnish Doctoral Programme in Computational Sciences and University of Auckland, Faculty of Science FDRF project 3624414/9844. The authors are grateful to an anonymous referee, whose comments helped clarify several ambiguities.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.cam.2011.09.035

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title = "Sparsity reconstruction in electrical impedance tomography: An experimental evaluation",

abstract = "We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ℓ1-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ℓ1-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. {\textcopyright} 2011 Elsevier B.V. All rights reserved.",

author = "Matthias Gehre and Tobias Kluth and Antti Lipponen and Bangti Jin and Aku Sepp{\"a}nen and Kaipio, {Jari P.} and Peter Maass",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The work of BJ was substantially supported by the Alexander von Humboldt Foundation through a postdoctoral researcher fellowship and partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and that of PM was supported by the German Science Foundation through grant MA 1657/18-1. AL, AS and JK were supported by the Academy of Finland (application number 213476, Finnish Programme for Centres of Excellence in Research 2006-2011), TEKES (Contract No. 40370/06), Finnish Doctoral Programme in Computational Sciences and University of Auckland, Faculty of Science FDRF project 3624414/9844. The authors are grateful to an anonymous referee, whose comments helped clarify several ambiguities. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Kaipio, Jari P.

AU - Maass, Peter

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N2 - We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ℓ1-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ℓ1-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. © 2011 Elsevier B.V. All rights reserved.

AB - We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ℓ1-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ℓ1-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. © 2011 Elsevier B.V. All rights reserved.

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Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

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