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Stochastic EM methods with variance reduction for penalised PET reconstructions

Kereta, Z; Twyman, R; Arridge, SR; Thielemans, K; Jin, B; (2021) Stochastic EM methods with variance reduction for penalised PET reconstructions. Inverse Problems , 37 (11) , Article 115006. 10.1088/1361-6420/ac2d74. Green open access

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Abstract

Expectation-maximisation (EM) is a popular and well-established method for image reconstruction in positron emission tomography (PET) but it often suffers from slow convergence. Ordered subset EM (OSEM) is an effective reconstruction algorithm that provides significant acceleration during initial iterations, but it has been observed to enter a limit cycle. In this work, we investigate two classes of algorithms for accelerating OSEM based on variance reduction for penalised PET reconstructions. The first is a stochastic variance reduced EM algorithm, termed as SVREM, an extension of the classical EM to the stochastic context that combines classical OSEM with variance reduction techniques for gradient descent. The second views OSEM as a preconditioned stochastic gradient ascent, and applies variance reduction techniques, i.e., SAGA and SVRG, to estimate the update direction. We present several numerical experiments to illustrate the efficiency and accuracy of the approaches. The numerical results show that these approaches significantly outperform existing OSEM type methods for penalised PET reconstructions, and hold great potential.

Type: Article
Title: Stochastic EM methods with variance reduction for penalised PET reconstructions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/ac2d74
Publisher version: https://doi.org/10.1088/1361-6420/ac2d74
Language: English
Additional information: © 2022 IOP Publishing. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0/).
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 Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Medical Sciences > Div of Medicine
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Medical Sciences > Div of Medicine > Department of Imaging
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 Computer Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/10136171
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