Three-dimensional image reconstruction for electrical impedance tomography

Very little work has been conducted on three-dimensional aspects of electrical impedance tomography (EIT), partly due to the increased computational complexity over the two-dimensional aspects of EIT. Nevertheless, extending EIT to three-dimensional data acquisition and image reconstruction may afford significant advantages such as an increase in the size of the independent data set and improved spatial resolution. However, considerable challenges are associated with the software aspects of three-dimensional EIT systems due to the requirement for accurate three-dimensional forward problem modelling and the derivation of three-dimensional image reconstruction algorithms. This paper outlines the work performed to date to derive a three-dimensional image reconstruction algorithm for EIT based on the inversion of the sensitivity matrix approach for a finite right circular cylinder. A comparison in terms of the singular-value spectra and the singular vectors between the sensitivity matrices for a three-dimensional cylinder and a two-dimensional disc has been performed. This comparison shows that the three-dimensional image reconstruction algorithm recruits more central information at lower condition numbers than the two-dimensional image reconstruction algorithm.