Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

Handle URI:
http://hdl.handle.net/10754/626198
Title:
Faster PET reconstruction with a stochastic primal-dual hybrid gradient method
Authors:
Ehrhardt, Matthias J.; Markiewicz, Pawel J.; Richtárik, Peter; Schott, Jonathan; Chambolle, Antonin; Schoenlieb, Carola-Bibiane
Abstract:
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.
KAUST Department:
Extreme Computing Research Center; Visual Computing Center (VCC)
Citation:
Ehrhardt MJ, Markiewicz PJ, Richtárik P, Schott J, Chambolle A, et al. (2017) Faster PET reconstruction with a stochastic primal-dual hybrid gradient method. Wavelets and Sparsity XVII. Available: http://dx.doi.org/10.1117/12.2272946.
Publisher:
SPIE
Journal:
Wavelets and Sparsity XVII
Conference/Event name:
Wavelets and Sparsity XVII 2017
Issue Date:
24-Aug-2017
DOI:
10.1117/12.2272946
Type:
Conference Paper
Sponsors:
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).
Additional Links:
https://www.spiedigitallibrary.org/conference-proceedings-of-spie/10394/2272946/Faster-PET-reconstruction-with-a-stochastic-primal-dual-hybrid-gradient/10.1117/12.2272946.full
Appears in Collections:
Conference Papers; Extreme Computing Research Center; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorEhrhardt, Matthias J.en
dc.contributor.authorMarkiewicz, Pawel J.en
dc.contributor.authorRichtárik, Peteren
dc.contributor.authorSchott, Jonathanen
dc.contributor.authorChambolle, Antoninen
dc.contributor.authorSchoenlieb, Carola-Bibianeen
dc.date.accessioned2017-11-23T11:51:29Z-
dc.date.available2017-11-23T11:51:29Z-
dc.date.issued2017-08-24en
dc.identifier.citationEhrhardt MJ, Markiewicz PJ, Richtárik P, Schott J, Chambolle A, et al. (2017) Faster PET reconstruction with a stochastic primal-dual hybrid gradient method. Wavelets and Sparsity XVII. Available: http://dx.doi.org/10.1117/12.2272946.en
dc.identifier.doi10.1117/12.2272946en
dc.identifier.urihttp://hdl.handle.net/10754/626198-
dc.description.abstractImage 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.en
dc.description.sponsorshipM. 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).en
dc.publisherSPIEen
dc.relation.urlhttps://www.spiedigitallibrary.org/conference-proceedings-of-spie/10394/2272946/Faster-PET-reconstruction-with-a-stochastic-primal-dual-hybrid-gradient/10.1117/12.2272946.fullen
dc.rightsArchived with thanks to Wavelets and Sparsity XVIIen
dc.titleFaster PET reconstruction with a stochastic primal-dual hybrid gradient methoden
dc.typeConference Paperen
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalWavelets and Sparsity XVIIen
dc.conference.date2017-08-06 to 2017-08-09en
dc.conference.nameWavelets and Sparsity XVII 2017en
dc.conference.locationSan Diego, CA, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment for Applied Mathematics and Theoretical Physics, University of Cambridge, , United Kingdomen
dc.contributor.institutionTranslational Imaging Group, CMIC, Department of Medical Physics and Biomedical Engineering, University College London, , United Kingdomen
dc.contributor.institutionCMAP, Ecole Polytechnique, CNRS, , , , Franceen
dc.contributor.institutionAlan Turing Institute, London, , United Kingdomen
dc.contributor.institutionSchool of Mathematics, University of Edinburgh, , United Kingdomen
dc.contributor.institutionDementia Research Centre, Institute of Neurology, University College, London, , , United Kingdomen
kaust.authorSchott, Jonathanen
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