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

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: Proceedings Volume 10394, Wavelets and Sparsity XVII. (pp. 103941O-1-103941O-11). SPIE: San Diego, CA, U S. Green open access

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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.

Type: Proceedings paper
Title: Faster PET reconstruction with a stochastic primal-dual hybrid gradient method
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States
ISBN-13: 9781510612457
Open access status: An open access version is available from UCL Discovery
DOI: 10.1117/12.2272946
Publisher version: http://dx.doi.org/10.1117/12.2272946
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Positron emission tomography, PET, total variation, convex optimization, primal-dual algorithms, saddle point problems, stochastic optimization, inverse problems
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Neurodegenerative Diseases
UCL > Provost and Vice Provost Offices > UCL BEAMS
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 SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
URI: https://discovery.ucl.ac.uk/id/eprint/10038693
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