A primal dual proximal point method of Chambolle-Pock algorithms for ℓ1-TV minimization problems in image reconstruction

Computed tomography (CT) image reconstruction problems can be solved by finding the minimizer of a suitable objective function. The objective function usually consists of a data fidelity term and a regularization term. Total variation (TV) minimization problems are widely used for solving incomplete data problems in CT image reconstruction. In this paper, we focus on the CT image reconstruction model which combines the TV regularization and ℓ₁ data error term. We introduce a primal dual proximal point method of Chambolle-Pock algorithm to solve the proposed optimization problem. We tested it on computer simulated data and the experiment results shown it exhibited good performance when used to few-view CT image reconstruction.