A hybrid stochastic-deterministic gradient descent algorithm for image reconstruction in cone-beam computed tomography

Abstract

There is a growing interest in algorithms for computed tomography (CT) reconstruction from a small number of projection measurements. In this paper, we propose an algorithm that is based on variance-reduced stochastic gradient descent (SGD). Variance-reduced SGD methods are a new class of stochastic optimization algorithms that have proved highly successful in solving large-scale optimization problems. These algorithms store a copy of the full gradient direction or stochastic gradient directions and use them in building update directions. We propose an algorithm for CT image reconstruction that starts off with variance-reduced SGD updates and gradually increases the batch size. As the algorithm approaches the solution and the batch size grows, the algorithm turns into a limited-memory quasi-Newton algorithm to exploit the curvature information in the vicinity of the solution. We apply the proposed algorithm on simulated and real cone-beam CT projections and compare it with several other algorithms. Our results show that the proposed algorithm is very fast and is able to reconstruct very high-quality images in a small number of iterations.