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

Matthias J. Ehrhardt; Pawel Markiewicz; Antonin Chambolle; Peter Richtárik; Jonathan Schott; Carola Bibiane Schönlieb

doi:10.1117/12.2272946

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

Matthias J. Ehrhardt
, Pawel Markiewicz
, Antonin Chambolle
, Peter Richtárik
, Jonathan Schott
, Carola Bibiane Schönlieb

Institute for Mathematical Innovation (IMI)

University of Cambridge
University College London
Centre national de la recherche scientifique
King Abdullah University of Science and Technology
University of Edinburgh
The Alan Turing Institute

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

12 Citations (SciVal)

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.

Original language	English
Title of host publication	Wavelets and Sparsity XVII
Publisher	SPIE
ISBN (Electronic)	9781510612457
DOIs	https://doi.org/10.1117/12.2272946
Publication status	Published - 1 Jan 2017
Event	Wavelets and Sparsity XVII 2017 - San Diego, USA United States Duration: 6 Aug 2017 → 9 Aug 2017

Publication series

Name	Proceedings of SPIE
Volume	10394

Conference

Conference	Wavelets and Sparsity XVII 2017
Country/Territory	USA United States
City	San Diego
Period	6/08/17 → 9/08/17

Funding

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 Math- ematics 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).

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

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10.1117/12.2272946

Cite this

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title = "Faster PET reconstruction with a stochastic primal-dual hybrid gradient method",

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.",

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AU - Richtárik, Peter

AU - Schott, Jonathan

AU - Schönlieb, Carola Bibiane

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

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