Efficient Jacobian Computations for Complex ECT/EIT Imaging

Markus Neumayer (), Thomas Suppan, Thomas Bretterklieber, Hannes Wegleiter and Colin Fox
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Markus Neumayer: Christian Doppler Laboratory for Measurement Systems for Harsh Operating Conditions, A-8010 Graz, Austria
Thomas Suppan: Christian Doppler Laboratory for Measurement Systems for Harsh Operating Conditions, 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
Colin Fox: Department of Physics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand

Mathematics, 2024, vol. 12, issue 7, 1-12

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.

Keywords: complex conductivity; quasi-static; FE simulation; Green’s function; Jacobian; tomography; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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