Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

  • Authors:

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

  • Affiliations:

  • Center for Industrial Mathematics, University of Bremen, D-28334 Bremen, Germany;Center for Industrial Mathematics, University of Bremen, D-28334 Bremen, Germany;Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, FIN-70211 Kuopio, Finland;Department of Mathematics and Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, 77843-3368 TX, USA;Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, FIN-70211 Kuopio, Finland;Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, FIN-70211 Kuopio, Finland and Department of Mathematics, University of Auckland, 38 Princes Street, 1142 Auckla ...;Center for Industrial Mathematics, University of Bremen, D-28334 Bremen, Germany

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2012

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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 @?^1-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 @?^1-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.