Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution inside an inhomogeneous distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. A hybrid method is proposed for solving the inverse problem for EIT, which combines the Krylov subspace and the Tikhonov regularization for double levels of regularization to the ill-posed problem. Numerical simulation results using the hybrid method are presented and compared to those from truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization. Experimental results with the hybrid method are also presented, indicating that the hybrid method can reduce the computation time, and improve the resolution of reconstructed images with the regularization parameter automatically chosen by the L-curve method.
lectrical 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.
This paper presents an adaptive multigrid method used in both the forward and inverse problems. The proposed method combines adaptive mesh and multigrid solution strategy to resolve the forward problem. The accuracy and efficiency of the former forward solver are improved by incorporating the above two procedures. For image reconstruction the regularized Gauss-Newton method combined with adaptive multigrid method can improve the spatial resolution of reconstructed images. Both experimental and simulated results are presented.
Athinoula A. Martinos Center for Biomedical Imaging