Joint Reconstruction of the Activity and the Attenuation in PET by Diffusion Posterior Sampling: a Feasibility Study

Abstract: This study introduces a novel framework for joint reconstruction of the activity and the attenuation (JRAA) in positron emission tomography (PET) using diffusion posterior sampling (DPS). By leveraging diffusion models (DMs), this approach directly addresses activity-attenuation dependencies, mitigating crosstalk issues prevalent in non-time-of-flight (TOF) settings. Experimental evaluations, conducted using 2-dimensional (2-D) XCAT phantom data, demonstrate that DPS significantly outperforms traditional maximum likelihood activity and attenuation (MLAA) methods, producing consistent and high-quality reconstructions even in the absence of TOF information. Ongoing work aims to extend our method to real 3-dimensional (3-D) data with encouraging preliminary findings.