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

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

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 (US)
Title of host publication	Wavelets and Sparsity XVII
Editors	Yue M. Lu, Dimitri Van De Ville, Dimitri Van De Ville, Manos Papadakis
Publisher	SPIE
ISBN (Electronic)	9781510612457
DOIs	https://doi.org/10.1117/12.2272946
State	Published - 2017
Event	Wavelets and Sparsity XVII 2017 - San Diego, United States Duration: Aug 6 2017 → Aug 9 2017

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	10394
ISSN (Print)	0277-786X
ISSN (Electronic)	1996-756X

Conference

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

Bibliographical note

Publisher Copyright:
© 2017 SPIE.

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

Ehrhardt, M. J., Markiewicz, P., Chambolle, A., Richtárik, P., Schott, J., & Schönlieb, C. B. (2017). Faster PET reconstruction with a stochastic primal-dual hybrid gradient method. In Y. M. Lu, D. Van De Ville, D. Van De Ville, & M. Papadakis (Eds.), Wavelets and Sparsity XVII Article 103941O (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 10394). SPIE. https://doi.org/10.1117/12.2272946

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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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Ehrhardt, MJ, Markiewicz, P, Chambolle, A, Richtárik, P, Schott, J & Schönlieb, CB 2017, Faster PET reconstruction with a stochastic primal-dual hybrid gradient method. in YM Lu, D Van De Ville, D Van De Ville & M Papadakis (eds), Wavelets and Sparsity XVII., 103941O, Proceedings of SPIE - The International Society for Optical Engineering, vol. 10394, SPIE, Wavelets and Sparsity XVII 2017, San Diego, United States, 08/6/17. https://doi.org/10.1117/12.2272946

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method. / Ehrhardt, Matthias J.; Markiewicz, Pawel; Chambolle, Antonin et al.
Wavelets and Sparsity XVII. ed. / Yue M. Lu; Dimitri Van De Ville; Dimitri Van De Ville; Manos Papadakis. SPIE, 2017. 103941O (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 10394).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Markiewicz, Pawel

AU - Chambolle, Antonin

AU - Richtárik, Peter

AU - Schott, Jonathan

AU - Schönlieb, Carola Bibiane

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N2 - 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.

AB - 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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Ehrhardt MJ, Markiewicz P, Chambolle A, Richtárik P, Schott J, Schönlieb CB. Faster PET reconstruction with a stochastic primal-dual hybrid gradient method. In Lu YM, Van De Ville D, Van De Ville D, Papadakis M, editors, Wavelets and Sparsity XVII. SPIE. 2017. 103941O. (Proceedings of SPIE - The International Society for Optical Engineering). doi: 10.1117/12.2272946

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

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