A Comparison of the Mutual Energy Concept with an Adjoint State Approach for Jacobian Calculation in ECT

Bernhard Brandstätter and Bernhard Kortschak

Christian Doppler Laboratory for Automotive Measurement Research

located at The Institute of Measurement and Measurement Signal Processing, Kopernikusgasse 24/4, A-8010, Graz, Austria, Email: brand@ieee.org

ABSTRACT

Iterative reconstruction methods based on a Gauss-Newton scheme require the efficient calculation of Jacobian matrices. In electrical capacitance systems this calculation can be carried out by means of a mutual energy concept, which is very similar to the reciprocity principle for electrical impedance tomography or by an adjoint variable method (AVM). A detailed comparison of both methods on the basis of test examples will be given in this paper.

Keywords Capacitance Tomography, Jacobian, adjoint variable method, mutual energy concept