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Efficient Jacobian Computations for Complex ECT/EIT Imaging

Author

Listed:
  • Markus Neumayer

    (Christian Doppler Laboratory for Measurement Systems for Harsh Operating Conditions, A-8010 Graz, Austria
    Institute of Electrical Measurement and Sensor Systems, Graz University of Technology, Inffeldgasse 23/II, A-8010 Graz, Austria)

  • Thomas Suppan

    (Christian Doppler Laboratory for Measurement Systems for Harsh Operating Conditions, A-8010 Graz, Austria
    Institute of Electrical Measurement and Sensor Systems, Graz University of Technology, Inffeldgasse 23/II, A-8010 Graz, Austria)

  • Thomas Bretterklieber

    (Institute of Electrical Measurement and Sensor Systems, Graz University of Technology, Inffeldgasse 23/II, A-8010 Graz, Austria)

  • Hannes Wegleiter

    (Christian Doppler Laboratory for Measurement Systems for Harsh Operating Conditions, A-8010 Graz, Austria
    Institute of Electrical Measurement and Sensor Systems, Graz University of Technology, Inffeldgasse 23/II, A-8010 Graz, Austria)

  • Colin Fox

    (Department of Physics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand)

Abstract

The reconstruction of the spatial complex conductivity σ + j ω ε 0 ε r from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. However, the necessary computation of the Jacobian is known to be computationally expensive, as standard techniques such as adjoint field methods require additional simulations. In this work, we show a more efficient way to computationally access the Jacobian matrix. In particular, the presented techniques do not require additional simulations, making the use of the Jacobian, free of additional computational costs.

Suggested Citation

  • Markus Neumayer & Thomas Suppan & Thomas Bretterklieber & Hannes Wegleiter & Colin Fox, 2024. "Efficient Jacobian Computations for Complex ECT/EIT Imaging," Mathematics, MDPI, vol. 12(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1023-:d:1366199
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