Methods for Calculating the Electrode Position Jacobian for Impedance Imaging

Electrical Impedance Tomography (EIT) or Electrical Resistivity Tomography (ERT) apply current and measure voltages at the boundary of a domain through electrodes. The movement or incorrect placement of electrodes may lead to modelling errors that result in signi_cant reconstructed image artifacts. These errors may be accounted for by allowing for electrode position estimates in the model.
Movement may be reconstructed through a _rst-order approximation, the electrode position Jacobian. A reconstruction that incorporates electrode position estimates and conductivity can signi_cantly reduce image artifacts. Conversely, if electrode position is ignored it can be di_cult to distinguish true conductivity changes from reconstruction artifacts which may increase the risk of a awed interpretation. In this work, we aim to determine the fastest, most accurate approach for estimating the electrode position Jacobian. Four methods of calculating the electrode position Jacobian were evaluated on a homogeneous halfspace. Results show that Fr_echet derivative and rank-one update methods are competitive in computational e_ciency but achieve di_erent solutions for certain values of contact impedance and mesh density.