Comparing Reconstruction Algorithms for Electrical Impedance Tomography

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Abstract
An improved electrical impedance tomographic reconstruction algorithm is presented that is generally guaranteed to converge. The algorithm is attractive for several reasons. A modified Newton-Raphson method varies a finite-element model of resistivities to fit a set of voltage measurements in a least-squared sense. Two procedures for calculating the Jacobian matrix are derived. One is standard, while the other is based on the compensation theorem. This second procedure is more efficient for computations, and just as accurate as the standard one. The inherent ill-conditioning in the approximate Hessian matrix of the linearized system is eliminated using the Marquardt method. Results from two-dimensional computer simulations are compared to four other reconstruction algorithms, which are based on methods proposed by other authors. The modified Newton-Raphson method provided significantly better reconstructions than any of the other methods. The algorithms compared are the perturbation, equipotential, iterative-equipotential, and the double-constraint methods. The modified Newton-Raphson method was found to be sensitive to measurement error, but future work in designing electrode-probing configurations is expected to reduce this sensitivity.

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