3D Conductivity Image Reconstruction Based on Electrical Impedance Tomography

The authors present the application of deterministic methods for the calculation of conductivity images in electrical impedance tomography. Reconstruction based on electrical impedance tomography is predominantly characterized as the solution of a 2D problem; however, this paper contains a description of the conductivity reconstruction procedure utilizing threedimensional models. Within electrical impedance tomography, the calculation of conductivity is realized using measured voltages on the electrodes placed at the edge of the examined object. In the course of the calculation process, an electric current source is connected to the sample. A direct current source enables us to obtain electrical conductivity distribution in the investigated object; with an alternating current source, we acquire the values of both the amplitude and the phase of the measured voltage and are thus able to obtain impedivity distribution. As a nonlinear inverse problem, the calculation of conductivity based on the measured voltage values is highly ill-posed. The reconstruction process is described as the minimization of a suitably selected function. In order to ensure stability of the solution, the Tikhonov regularization method or Total variation method is used, the regularization term complements the objective function. The paper describes a mathematical model of the solved 3D conductivity reconstruction problem.