Twyman, Robert;
Arridge, Simon;
Kereta, Zeljko;
Jin, Bangti;
Brusaferri, Ludovica;
Ahn, Sangtae;
Stearns, Charles W;
... Thielemans, Kris; + view all
(2022)
An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalised 3D PET Image Reconstruction.
IEEE Transactions on Medical Imaging
10.1109/tmi.2022.3203237.
(In press).
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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.
| Type: | Article |
|---|---|
| Title: | An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalised 3D PET Image Reconstruction |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/tmi.2022.3203237 |
| Publisher version: | https://doi.org/10.1109/tmi.2022.3203237 |
| Language: | English |
| Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Image reconstruction, Convergence, Positron emission tomography, Linear programming, Stochastic processes, Optimization, Indexes |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10155269 |
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