Model-aware Newton-type inversion scheme for electrical impedance tomography

Abstract

Electrical impedance tomography is a non-invasive method for imaging the electrical conductivity of an object from voltage measurements on its surface. This inverse problem suffers in three respects: It is highly nonlinear, severely ill-posed and highly under-determined. To obtain yet reasonable reconstructions, maximal information needs to be gathered from the model and extracted from the data in all stages of the reconstruction procedure. We will present a holistic reconstruction framework which estimates the unknown model-specific parameters, i.e. background conductivity, contact impedance, and noise level, before solving the full nonlinear problem with a Newton-type method. Therein, a novel conductivity transformation decreases nonlinearity while a weighting scheme resolves the under-determinedness by promoting the reconstruction of piecewise constant conductivities. This way we increase robustness, speed, and reconstruction accuracy. Moreover, our method is easy to use and applies to a wide range of settings as it is free of design parameters. Being an absolute imaging method, no measured calibration data is required. We demonstrate the performance of this concept numerically for simulated and measured data.

Structural-functional lung imaging using a combined CT-EIT and a Discrete Cosine Transformation reconstruction method

“…Most of them have been developed for special purposes, e.g. absolute EIT imaging 23 , compensation of motion artifacts 24 , compensation for faulty electrodes 25 , 3D imaging 26 , methods considering temporal correlation to reduce image noise 27 or utilizing Kalman filter approaches to track fast changes in conductivity distribution 28 . Other algorithms are based on expert defined figures of merit 29 or on eigenimages from CT data as training sets 30 .…”

Geophysical Applications of Electrical Impedance Tomography

“…The intermediate k = 0.5 has been observed to distribute artifacts evenly throughout the image and gives updates that are almost independent of discretization geometry (Winkler and Rieder, 2015).…”

“…Experimental measurement of contact impedance then incorporates wiring resistance, electrode properties and any transport phenomena across the electrodes. Impedance imaging hardware can collect data for an estimate of contact impedance by measuring at stimulus electrodes (two electrode measurements) and combining this with the normally collected four electrode measurements to calculate an estimate of contact impedance Winkler and Rieder, 2015).…”

“…Contact impedance and full movement vectors could, in principle, be estimated as columns in the Jacobian. Contact impedance and the conductivity distribution have been simultaneously reconstructed for impedance images Heikkinen et al, 2002;Winkler and Rieder, 2015).…”

“…(Winkler and Rieder, 2015) have S J,σ = S/σ 0 : we note that for a homogeneous initial conductivity σ 0 , this amounts to a scaling of the hyperparameter λ 2 → λ 2 /σ 0 .…”