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PET Reconstruction with non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence

Bousse, A; Cordurier, M; Emond, E; Thielemans, K; Hutton, B; Irarrazaval, P; Visvikis, D; (2019) PET Reconstruction with non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence. IEEE Transactions on Medical Imaging 10.1109/TMI.2019.2920109. (In press). Green open access

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Abstract

Standard positron emission tomography (PET) reconstruction techniques are based on maximum-likelihood (ML) optimization methods, such as the maximum-likelihood expectation-maximization (MLEM) algorithm and its variations. Most of these methodologies rely on a positivity constraint on the activity distribution image. Although this constraint is meaningful from a physical point of view, it can be a source of bias for low-count/high-background PET, which can compromise accurate quantification. Existing methods that allow for negative values in the estimated image usually utilize a modified loglikelihood, and therefore break the data statistics. In this work we propose to incorporate the positivity constraint on the projections only, by approximating the (penalized) log-likelihood function by an adequate sequence of objective functions that are easily maximized without constraint. This sequence is constructed such that there is hypo-convergence (a type of convergence that allows the convergence of the maximizers under some conditions) to the original log-likelihood, hence allowing us to achieve maximization with positivity constraint on the projections using simple settings. A complete proof of convergence under weak assumptions is given. We provide results of experiments on simulated data where we compare our methodology with the alternative direction method of multipliers (ADMM) method, showing that our algorithm converges to a maximizer which stays in the desired feasibility set, with faster convergence than ADMM. We also show that this approach reduces the bias, as compared with MLEM images, in necrotic tumors—which are characterized by cold regions surrounded by hot structures—while reconstructing similar activity values in hot regions.

Type: Article
Title: PET Reconstruction with non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TMI.2019.2920109
Publisher version: https://doi.org/10.1109/TMI.2019.2920109
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Image reconstruction, Maximum likelihood estimation, Positron emission tomography, Convergence, Linear programming, Optimization, Phase locked loops, PET Imaging, Penalized Maximum-Likelihood Image Reconstruction, Constrained Optimization, Hypo-Convergence
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
URI: https://discovery.ucl.ac.uk/id/eprint/10076004
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