Solving the electrical impedance tomography inverse problem for logarithmic conductivity: Numerical sensitivity

Abstract

Purpose

In the context of electrical impedance tomography (EIT), this paper aims to evaluate limitations of estimating conductivity or resistivity, as well as the improvements achieved with the use of an alternate description of the solution space, the logarithmic conductivity.

Design/methodology/approach

A quantitative analysis is performed, solving the inverse EIT problem by using the Gauss–Newton and non-linear conjugate gradient methods for a numerical phantom of 15 elements. A property of symmetry is studied for the direct EIT problem for a phantom of 385,601 elements.

Findings

Solving the inverse EIT problem in logarithmic conductivity is more robust to the initial guess, as solutions are kept within physical bounds (conductivity positiveness). Also, convergence is faster and less dependent on the final values of the estimates.

Research limitations/implications

Logarithmic conductivity provides an advantageous description of the solution space for the EIT inverse problem. Similar estimation problems might be subject to analogous conclusions.

Originality/value

This study provides a novel analysis, quantitatively comparing the effect of different variables to solve the inverse EIT problem.

Citation

Pellegrini, S.P., Trigo, F.C. and Lima, R.G. (2018), "Solving the electrical impedance tomography inverse problem for logarithmic conductivity: Numerical sensitivity", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 37 No. 2, pp. 681-690. https://doi.org/10.1108/COMPEL-11-2016-0501