Model-Based Deep Learning PET Image Reconstruction Using Forward-Backward Splitting Expectation Maximisation

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Abstract

We propose a forward backward splitting algorithm to integrate deep learning into maximum-a-posteriori (MAP) PET image reconstruction. The MAP reconstruction is split into regularisation, expectation-maximisation (EM) and a weighted fusion. For regularisation, use of either a Bowsher prior (using Markov-random fields) or a residual learning unit (using convolutional-neural networks) were considered. For the latter, our proposed forward backward splitting expectation-maximisation (FBSEM), accelerated with ordered-subsets (OS), was unrolled into a recurrent-neural network in which network parameters (including regularisation strength) are shared across all states and learned during PET reconstruction. Our network was trained and evaluated using PET-only (FBSEM-p) and PET-MR (FBSEM-pm) datasets for low-dose simulations and short-duration in-vivo brain imaging. It was compared to OSEM, Bowsher MAPEM and a post-reconstruction U-Net denoising trained on the same PET-only (Unet-p) or PET-MR (Unet-pm) datasets. For simulations, FBSEM-p(m) and Unet-p(m) nets achieved a comparable performance, on average, 14.4% and 13.4% normalised root-mean square error (NRMSE), respectively; and both outperformed OSEM and MAPEM methods (with 20.7% and 17.7% NRMSE respectively). For in-vivo datasets, FBSEM-p(m), Unet-p(m), MAPEM and OSEM methods achieved average root-sum-of-squared errors of 3.9%, 5.7%, 5.9% and 7.8% in different brain regions, respectively. In conclusion, the studied U-Net denoising method achieved a comparable performance to a representative implementation of FBSEM net.
Original languageEnglish
JournalTransactions on Radiation and Plasma Medical Sciences
Early online date23 Jun 2020
DOIs
Publication statusE-pub ahead of print - 23 Jun 2020

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