Ordered subsets acceleration using relaxed momentum for X-ray CT image reconstruction

Statistical image reconstruction in X-ray CT can provide decent images even with low dose, but requires substantial computation time. Recently, we have proposed combining ordered subsets (OS) methods and Nesterov's momentum technique for accelerated X-ray CT image reconstruction. We have observed rapid convergence speed of the proposed algorithms in our experiments, but sometimes encountered unstable behavior. Therefore, we introduce a diminishing step size rule, called a relaxed momentum approach, to stabilize the algorithm, while preserving the fast convergence rate. We use a real 3D CT scan to show that the proposed approach can achieve both fast convergence rate and stability.