An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalized 3D PET Image Reconstruction

Journal article


Twyman, R., Arridge, S., Kereta, Z., Jin, B., Brusaferri, L., Ahn, S., Stearns, C.W., Hutton, B., Burger, I.A., Kotasidis, F. and Thielemans, K. (2023). An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalized 3D PET Image Reconstruction. IEEE Transactions on Medical Imaging. pp. 29 - 41. https://doi.org/10.1109/tmi.2022.3203237
AuthorsTwyman, R., Arridge, S., Kereta, Z., Jin, B., Brusaferri, L., Ahn, S., Stearns, C.W., Hutton, B., Burger, I.A., Kotasidis, F. and Thielemans, K.
Abstract

Penalised PET image reconstruction algorithms are often accelerated during early iterations with the use of subsets. However, these methods may exhibit limit cycle behaviour at later iterations due to variations between subsets. Desirable converged images can be achieved for a subclass of these algorithms via the implementation of a relaxed step size sequence, but the heuristic selection of parameters will impact the quality of the image sequence and algorithm convergence rates. In this work, we demonstrate the adaption and application of a class of stochastic variance reduction gradient algorithms for PET image reconstruction using the relative difference penalty and numerically compare convergence performance to BSREM. The two investigated algorithms are: SAGA and SVRG. These algorithms require the retention in memory of recently computed subset gradients, which are utilised in subsequent updates. We present several numerical studies based on Monte Carlo simulated data and a patient data set for fully 3D PET acquisitions. The impact of the number of subsets, different preconditioners and step size methods on the convergence of regions of interest values within the reconstructed images is explored. We observe that when using constant preconditioning, SAGA and SVRG demonstrate reduced variations in voxel values between subsequent updates and are less reliant on step size hyper-parameter selection than BSREM reconstructions. Furthermore, SAGA and SVRG can converge significantly faster to the penalised maximum likelihood solution than BSREM, particularly in low count data.

Year2023
JournalIEEE Transactions on Medical Imaging
Journal citationpp. 29 - 41
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
ISSN0278-0062
1558-254X
Digital Object Identifier (DOI)https://doi.org/10.1109/tmi.2022.3203237
Web address (URL)http://dx.doi.org/10.1109/tmi.2022.3203237
Publication dates
Online31 Aug 2022
Publication process dates
Deposited16 Feb 2024
Publisher's version
License
File Access Level
Open
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