Comparison of the Newton-Raphson and the spectral expansion impedance tomography reconstruction algorithms

Impedance tomography reconstruction algorithms estimate the impedance distribution of a body segment from impedance measurements between electrodes placed on the surface of the body. Two such algorithms, the modified Newton-Raphson algorithm and the reconstruction procedure offered by the spectral analysis method are compared both numerically and analytically. It is found that if the two methods are regularised equivalently, then the spectral reconstruction is identical to one step of the Newton-Raphson algorithm. The formulas of the equivalent regularisation are given. This finding allows the transfer of regularisation methods between the two reconstruction algorithms.