AN ITERATIVE NEWTON-RAPHSON METHOD TO SOLVE THE INVERSE ADMITTIVITY PROBLEM

By applying electrical currents to the exterior of a body using electr odes and measuring the voltages developed on these electrodes, it is p ossible to reconstruct the electrical properties inside the body. This technique is known as electrical impedance tomography, The problem is nonlinear and ill conditioned meaning that a large perturbation in th e electrical properties far away from the electrodes produces a small voltage change on the boundary of the body, This paper describes an it erative reconstruction algorithm that yields approximate solutions of the inverse admittivity problem in two dimensions. By performing multi ple iterations, errors in the conductivity and permittivity reconstruc tions that result from a linearized solution to the problem are decrea sed. A finite-element forward-solver, which predicts voltages on the b oundary of the body given knowledge of the applied current on the boun dary and the electrical properties within the body, is required at eac h step of the reconstruction algorithm. Reconstructions generated from numerical data are presented that demonstrate the capabilities of thi s algorithm.