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arXiv · 2407.17135

Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction

Marco Mauritz·Benedikt Wirth
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Abstract

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET). These inverse problems are typically reconstructed via Bayesian methods. A natural question then is whether and how the reconstruction converges as the signal-to-noise ratio tends to infinity and how this convergence interacts with other parameters such as the detector size. In this article we carry out a corresponding variational analysis for the exemplary Bayesian reconstruction functional from [arXiv:2311.17784,arXiv:1902.07521], which considers dynamic PET imaging (i.e.\ the object to be reconstructed changes over time) and uses an optimal transport regularization.

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Marco Mauritz, Benedikt Wirth. 2024-07-24. Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction. https://arxiv.org/abs/2407.17135

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