Linearized solution to electrical impedance tomography based on the Schur conjugate gradient method

Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution of an inhomogeneous medium, usually by injecting a current at the periphery of an object and measuring the resulting changes in voltage. The conjugate gradient (CG) method is one of the most popular methods applied for image reconstruction, although its convergence rate is low. In this paper, an advanced version of the CG method, i.e. the Schur conjugate gradient (Schur CG) method, is used to solve the inverse problem for EIT. 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. This paper discusses the strategies of choosing parameters. Simulation results using the Schur CG algorithm are presented and compared with the conventional CG algorithm. Experimental results obtained by the Schur CG algorithm are also presented, indicating that the Schur CG algorithm can reduce the computational time and improve the quality of image reconstruction with the selected parameters.

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