Reduction of Staircase Effect With Total Generalized Variation Regularization for Electrical Impedance Tomography

Abstract

Image reconstruction in electrical impedance tomography is an ill-posed inverse problem. To address this problem, regularization methods such as Tikhonov regularization and total variation regularization have been adopted. However, the image is over-smoothed when reconstructing with the Tikhonov regularization and staircase effect appears in the image when using the total variation regularization. In this paper, the total generalized variation regularization method which combines the first-order and the second-order derivative terms to perform as the regularization term is proposed to cope with the above problems. The weight between the two derivative terms is adjusted by the weighting factors. Chambolle-Pock primal-dual algorithm, an efficient iterative algorithm to handle optimization problem and solve dual problem, is developed. Simulation and experiments are performed to verify the performance of the total generalized variation regularization method against other regularization methods. Besides, the relative error and correlation coefficient are also calculated to estimate the proposed regularization methods quantitatively. The results indicate that the staircase effect is effectively reduced and the sharp edge is well-preserved in the reconstructed image.