In computed tomography (CT), the total variation (TV) constrained algebraic reconstruction technique (ART) can obtain better reconstruction quality when the projection data are sparse and noisy. However, the ART-TV algorithm remains time-consuming since it requires large numbers of iterations, especially for the reconstruction of high-resolution images. In this work, we propose a fast algorithm to calculate the system matrix for line intersection model and apply this algorithm to perform the forward-projection and back-projection operations of the ART. Then, we utilize the parallel computing techniques of multithreading and graphics processing units (GPU) to accelerate the ART iteration and the TV minimization, respectively. Numerical experiments show that our proposed parallel implementation approach is very efficient and accurate. For the reconstruction of a 2048 × 2048 image from 180 projection views of 2048 detector bins, it takes about 2.2 seconds to perform one iteration of the ART-TV algorithm using our proposed approach on a ten-core platform. Experimental results demonstrate that our new approach achieves a speedup of 23 times over the conventional single-threaded CPU implementation that using the Siddon algorithm.
Keywords: Computed tomography (CT); algebraic reconstruction technique; image reconstruction; parallel computing; total variation.