Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.
|Original language||English (US)|
|Title of host publication||Wavelets and Sparsity XVII|
|Publisher||SPIE-Intl Soc Optical Eng|
|State||Published - Aug 24 2017|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: M. J. E. and C.-B. S. acknowledge support from Leverhulme Trust project \Breaking the non-convexity barrier", EPSRC grant \EP/M00483X/1", EPSRC centre \EP/N014588/1", the Cantab Capital Institute for the Mathematics of Information, and from CHiPS (Horizon 2020 RISE project grant). Moreover, C.-B. S. is thankful for support by the Alan Turing Institute. P. M. was supported by the Medical Research Council (MR/N025792/1) and AMYPAD (European Commission project ID: ID115952, H2020-EU.3.1.7. - Innovative Medicines Initiative 2). A. C. benefited from a support of the ANR, \EANOI" Project I1148 / ANR-12-IS01-0003 (joint with FWF). Part of this work was done while he was hosted in Churchill College and DAMTP, Centre for Mathematical Sciences, University of Cambridge, thanks to a support of the French Embassy in the UK and the Cantab Capital Institute for Mathematics of Information. P. R. acknowledges the support of EPSRC Fellowship in Mathematical Sciences \EP/N005538/1" entitled \Randomized algorithms for extreme convex optimization". The computations have been made on a GPU that was kindly made available by the NVIDIA GPU Grant Program. The Florbetapir PET tracer was provided by AVID Radiopharmaceuticals (a wholly owned subsidiary of Eli Lilly & Co).