Pm. Edic et al., AN ITERATIVE NEWTON-RAPHSON METHOD TO SOLVE THE INVERSE ADMITTIVITY PROBLEM, IEEE transactions on biomedical engineering, 45(7), 1998, pp. 899-908
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.