Model-Aware Newton-Type Inversion Scheme For Electrical Impedance Tomography

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.