Stochastic Variance Reduction Optimisation Algorithms Applied to Iterative PET Reconstruction

Abstract

Penalised PET image reconstruction methods are often accelerated with the use of only a subset of the data at each update. It is known that many subset algorithms, such as Ordered Subset Expectation Maximisation, do not converge to a single solution but to a limit cycle, which can lead to variations between subsequent image estimates. A new class of stochastic variance reduction optimisation algorithms have been recently proposed for general optimisation problems. These methods aim to reduce the subset update variance by incorporating previous subset gradients into the update direction computation. This work applies three of these algorithms to iterative PET penalised reconstruction and exhibits superior performance to standard deterministic reconstruction methods after only a few epochs.