An image reconstruction algorithm based on preconditioned LSQR for 3D EIT

Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current-voltage measurements on its boundary. Regularization is an effective method for the solution of such ill-posed inverse problems. The aim of this work is to explore more effective regularization-based solutions through the application of preconditioned LSQR (PLSQR) to the study of 3D EIT reconstruction. Four different subspace splitting methods, i.e., SVD, wavelet transform, cosine transform schemes and Krylov subspace, are presented to the design of the preconditioners for the problem. Amongst the four applied subspace splitting schemes, the SVD-based preconditioner yields the best convergence rate and outperforms the other three in seeking the solutions. The PLSQR method is also evaluated and compared with other algorithms such as LSQR without preconditioning and PCG methods. Moreover, the proposed method is testified in 3D lung EIT reconstruction in order to monitor lung ventilation. The results from this investigation suggest that the PLSQR is a useful 3D reconstruction method with high time efficiency and stability.