Accelerating X-ray CT ordered subsets image reconstruction with Nesterov’s first-order methods

Low-dose X-ray CT can reduce the risk of cancer to patients. However, it requires computationally expensive statistical image reconstruction methods for improved image quality. Iterative algorithms require long compute times, so we focus on algorithms that “converge” in few iterations. This paper proposes to apply ordered subsets (OS) methods to Nesterov’s fast firstorder methods for 3D X-ray CT problems. Nesterov’s algorithms use previous iterates to provide momentum towards the optimum and thus achieve a fast convergence rate of O(1/n), where n counts the number of iterations. We also propose to use separable quadratic surrogates (SQS) (with a non-uniform (NU) approach) in Nesterov’s algorithms. We use a real patient helical CT scan to show that the proposed algorithms converge rapidly, and we investigate the behavior of OS methods in Nesterov’s algorithms.