Evaluation of convergence speed of a modified Nesterov gradient method for CT reconstruction

In solving statistical iterative reconstruction problems, gradient-based algorithms are more amenable to parallel computing hardware such as GPUs and hence, can be made to have lower computation cost per iteration. However, they typically require more iterations to converge to a useful image. Among various acceleration techniques, algorithms proposed by Nesterov have proven to achieve an optimal convergence rate from certain theoretical perspectives. The Nesterov algorithms have shown potential to accelerate convergence speeds in several convex optimization problems such as compressed sensing reconstruction. In this paper, we introduce a modified Nesterov gradient (MNG) algorithm to CT model-based iterative reconstruction (MBIR) with an edge-preserving prior adjusted for clinical applications. MNG leverages an optimization concept similar to Nesterov´s original algorithm but employs a surrogate function to simplify the selection of the step size parameters. CT images in this manuscript were produced using both a computer simulation and a real dataset from a GE 64-slice scanner. The convergence rate of MNG is compared with conventional gradient descent (GD) and nonlinear conjugate gradient (NCG) methods. We also investigated combining the proposed algorithm with a ramp-filter-based preconditioner to further accelerate the convergence. Our results suggest that MNG significantly accelerates convergence compared to GD in both non-preconditioned and preconditioned cases.