A topological approach to positron emission particle tracking for finding multiple particles in high noise environments.

Positron emission particle tracking (PEPT) is an advanced imaging technique that accurately tracks the three-dimensional spatial coordinates of a radioactively-labelled particle with sub-millimetre and sub-millisecond precision. By detecting back-to-back 511 keV gamma rays from positron-electron annihilation coincidence events, PEPT can locate particles within highly dense, opaque systems such as fluidised beds, rotating drums, and mills. Despite the progress made in enhancing the precision and accuracy of PEPT, simultaneous multiple particle tracking remains a significant challenge, particularly in high-noise environments. This paper introduces T-PEPT, a novel algorithm that leverages topological data analysis-a relatively new field of applied mathematics that explores the underlying 'shape' of data through techniques like persistence homology. By creating simplicial complexes and applying persistence homology to PEPT point data, T-PEPT demonstrates highly effective performance in multiple-particle tracking, especially in scenarios with high noise. When benchmarked against existing PEPT algorithms using a widely recognised standard framework, T-PEPT consistently maintains sub-millimetre spatial and sub-millisecond temporal precision in nearly all cases, demonstrating its robustness and accuracy. For Data availability for T-PEPT, please use the GitHub repository: https://github.com/uob-positron-imaging-centre/pept .