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

24 August 2017 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

Proceedings Volume 10394, Wavelets and Sparsity XVII; 103941O (2017) https://doi.org/10.1117/12.2272946
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

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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Matthias J. Ehrhardt, Pawel Markiewicz, Antonin Chambolle, Peter Richtárik, Jonathan Schott, and Carola-Bibiane Schönlieb "Faster PET reconstruction with a stochastic primal-dual hybrid gradient method", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941O (24 August 2017); https://doi.org/10.1117/12.2272946

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