The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography

Source abstract

The factorization method is a tool for recovering inclusions inside a body when the Neumann-to-Dirichlet operator, which maps applied currents to measured voltages, is known. In practice this information is never at hand due to the discreteness and physical properties of the measurement devices. The complete electrode model of impedance tomography includes these physical characteristics but leads to a finite-dimensional data set, called the resistivity matrix. The main result of this work is an approximation link relating the resistivity matrix to the Neumann-to-Dirichlet operator in the $L^2$-operator norm. This result allows us to extend the factorization method to the framework of real-life electrode measurements using a regularized series criterion which is easy to implement in practice. The truncation index of the sequence criterion, which represents the stopping index of the regularization scheme, can be computed solely from the measured, perturbed, and finite-dimensional data. The functionality of the method is demonstrated through numerical experiments.