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    Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

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    Type
    Article
    Authors
    Gehre, Matthias
    Kluth, Tobias
    Lipponen, Antti
    Jin, Bangti
    Seppänen, Aku
    Kaipio, Jari P.
    Maass, Peter
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2012-02
    Permanent link to this record
    http://hdl.handle.net/10754/599683
    
    Metadata
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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.
    Citation
    Gehre M, Kluth T, Lipponen A, Jin B, Seppänen A, et al. (2012) Sparsity reconstruction in electrical impedance tomography: An experimental evaluation. Journal of Computational and Applied Mathematics 236: 2126–2136. Available: http://dx.doi.org/10.1016/j.cam.2011.09.035.
    Sponsors
    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.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2011.09.035
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2011.09.035
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