An electrical impedance tomography algorithm with well-defined spectral properties

A well-established reconstruction algorithm for electrical impedance tomography uses a finite-element method to model the forwards problem using Neumann boundary conditions. The reconstruction is then obtained by solving the inverse problem through an iterative non-linear least-squares fit of the model electrode voltages to the measured voltages. It is also usual to apply Tikhonov regularization to improve the condition of the inverse problem. However, such regularization introduces artefacts into the solution estimate. We present a quasi-single-step reconstruction technique based on a weakly regularized solution constructed from the final Jacobian of the standard iterative scheme, with filtering to act as a 'mollifier'. This reconstruction has well-defined spectral properties, since it approximates a filtered version of the original impedance distribution. Some illustrative results are given for 2D resistance tomography.