Direct image reconstruction for 3-D electrical resistance tomography by using the factorization method and electrodes on a single plane

A direct reconstruction method for three-dimensional (3-D) electrical resistance tomography was introduced by using the factorization method. Compared with the traditional image reconstruction algorithms based on the sensitivity/Jacobian matrix, the conductivity distribution in any part of the 3-D region of interest can be obtained directly and independently. A new way to calculate the Neumann-to-Dirichlet map was also introduced by using the adjacent current pattern. Several phantoms were constructed for image reconstruction in three dimensions. The data were collected from 16 electrodes on a single cross section, which can be only used to produce two-dimensional images in the literature. Neither matrix inversion nor iteration was used in the process of image reconstruction. The reconstructed results validated the feasibility of the method.