The integrated acceleration of the Chambolle-Pock algorithm applied to constrained TV minimization in CT image reconstruction

ABSTRACT Background and Objective: The constrained, total variation (TV) minimization algorithm has been applied in computed tomography (CT) for more than 10 years to reconstruct images accurately from sparse-view projections. Chambolle-Pock (CP) algorithm framework has been used to derive the algorithm instance for the constrained TV minimization programme. However, the ordinary CP (OCP) algorithm has slower convergence rate and each iteration is also time-consuming. Thus, we investigate the acceleration approaches for achieving fast convergence and high-speed reconstruction. Methods: To achieve fast convergence rate, we propose a new algorithm parameters setting approach for OCP. To achieve high-speed reconstruction in each iteration, we use graphics processing unit (GPU) to speed-up the two time-consuming operations, projection and backprojection. Results: We evaluate and validate our acceleration approaches via two-dimensional (2D) reconstructions of a low-resolution Shepp–Logan phantom from noise-free data and a high-resolution Shepp–Logan phantom from noise-free and noisy data. For the three-specific imaging cases considered here, the convergence process are speeded up for 89, 9 and 81 times, and the reconstruction in each iteration maybe speeded up for 120, 340 and 340 times, respectively. Totally, the whole reconstructions for the three cases are speeded up for about 10,000, 3060 and 27,540 times, respectively. Conclusions: The OCP algorithm maybe tremendously accelerated by use of the improved algorithm parameters setting and use of GPU. The integrated acceleration techniques make the OCP algorithm more practical in the CT reconstruction area.