A fast three-dimensional image reconstruction method for ERT

Electrical resistance tomography (ERT) aims to estimate the electrical properties at the interior of an object from current-voltage measurements on its boundary. Although two-dimensional model is commonly used in most research, it cannot satisfy practical needs. In this paper, three different electrode structures in three-dimension (3D) were proposed and compared. An advanced version of the conjugate gradient (CG) method, i.e. the Schur CG method, is used to solve the inverse problem for 3D ERT. The solution space is divided into two subspaces. The main part of the solution lies in the coarse subspace, which can be calculated directly and its corresponding correction term with a small norm can be solved in the Schur complement subspace. In order to improve the disadvantage of ill-posed for EIT problem, we also investigate three different multilayer electrode structures for 3D models. Experimental results obtained by the Schur CG algorithm are also presented, indicating that the Schur CG algorithm can improve the quality of reconstructed image and real time performance.