Electrical impedance tomography: regularized reconstruction using a variance uniformization constraint

Abstract

This paper presents a new regularization approach to the ill-posed inverse problem of electrical impedance tomography (EIT). The main focus of the communication is on the choice of the regularization matrix and of the regularization parameters. To select the regularization matrix the authors use a variance uniformization criterion so as to distribute uniformly the effect of the measurement noise over the whole estimate. Then, adequate values of the regularization parameters are determined from the observed data using ordinary cross validation (OCV). For practical reasons, linearized equations of the direct problem are used in this study. However, the technique can be extended to methods that solve the nonlinear direct problem in an iterative manner.