Numerical Solution of the Inverse Problem of Electrical Impedance Tomography Using the Iteration Method

A computational algorithm has been developed for solving the inverse problem of electricalimpedance tomography in a complete electrode model, which is an inverse coefficient problem fora difference scheme built on unstructured grids for an elliptic equation with integro-differentialboundary conditions. The iteration algorithm is based on the iterative regularized Gauss–Newtonmethod in which the inverse matrix of the main matrix of the system of linear equations iscalculated; the derivatives of the main matrix whose coefficients depend linearly on conductivityare found analytically. The implementation of the computational algorithm is performed for thetwo-dimensional case of a 16-electrode disk model with one insert. The influence of the choice ofthe initial approximation and the error in the input data on the convergence of the iterationprocess has been studied.