A Bayesian model for dynamic mass reconstruction from PET listmode data

2023/11/29 by Mauritz, Marco, Schmitzer, Bernhard, Wirth, Benedikt · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2311.17784

Abstract

Positron emission tomography (PET) is a classical imaging technique to reconstruct the mass distribution of a radioactive material. If the mass distribution is static, this essentially leads to inversion of the X-ray transform. However, if the mass distribution changes temporally, the measurement signals received over time (the so-called listmode data) belong to different spatial configurations. We suggest and analyse a Bayesian approach to solve this dynamic inverse problem that is based on optimal transport regularization of the temporally changing mass distribution. Our focus lies on a rigorous derivation of the Bayesian model and the analysis of its properties, treating both the continuous as well as the discrete (finitely many detectors and time binning) setting.

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