Joint Reconstruction of Activity and Attenuation in PET by Diffusion Posterior Sampling in Wavelet Coefficient Space

Attenuation correction (AC) is necessary for accurate activity quantification in positron emission tomography (PET). Conventional reconstruction methods typically rely on attenuation maps derived from a co-registered computed tomography (CT) or magnetic resonance (MR) scan. However, this additional scan may complicate the imaging workflow, introduce misalignment artifacts and increase radiation exposure. In this paper, we propose a joint reconstruction of activity and attenuation (JRAA) approach that eliminates the need for auxiliary anatomical imaging by relying solely on emission data. This framework combines wavelet diffusion model (WDM) and diffusion posterior sampling (DPS) to reconstruct fully three-dimensional (3-D) data. Experimental results on simulated data show our method outperforms maximum likelihood activity and attenuation (MLAA) and MLAA-UNet with U-Net-based post processing, and yields high-quality noise-free reconstructions across various count settings with time-of-flight (TOF). It is also able to reconstruct non-TOF data, although the reconstruction quality significantly degrades in low-count (LC) conditions, limiting its practical effectiveness in such settings. Nonetheless, a non-TOF Biograph mMR real data reconstruction with joint scatter estimation highlights the potential of the method for clinical applications. This approach represents a step towards stand-alone PET imaging by reducing the dependence on anatomical modalities while maintaining quantification accuracy, even in LC scenarios when TOF information is available. Our code is available on GitHub at https://github.com/clemphg/jraa-dps.