List-mode quantitative joint reconstruction of activity and attenuation maps in Time-of-Flight PET

Quantitative PET imaging requires accurate determination of patient-specific attenuation maps, which remains challenging on hybrid PET/MRI systems owing to the lack of a direct relationship between MR image intensity and attenuation coefficients. The aim of the present study is to develop a list-mode based algorithm for accurate and robust attenuation correction of PET data using time-of-flight (TOF) emission information. We analyze and address the challenges of list-mode emission-based maximum-likelihood joint estimation of activity and attenuation (LM-MLAA) in state-of-the-art PET imaging. The proposed method exploits a rapid on-the-fly system matrix calculation algorithm based on elliptic integrals while updating the attenuation map from accumulating list-mode coincidences to achieve accelerated image reconstruction. The scattering compensation is incorporated inside it using an iterative approach in such that the current estimation of attenuation map used on a course grid sampling scattering points to make an estimate of scattering. The performance of the proposed LM-MLAA approach was evaluated on Monte Carlo simulations of a phantom at different time resolutions. The contrast and noise for hot and cold regions on reconstructed images at different time resolutions were analysed. The estimated attenuation map exhibits resilience against noise, effectively eliminates high-frequency cross-talk even in the absence of prior information on attenuation coefficients, and enables discrimination among different anatomical regions in the reconstructed image. The error in the mean estimated attenuation coefficients after 50 iterations was similar to 2% in water and similar to -14% in Teflon regions for TOF resolutions corresponding to those of most current commercial PET systems (similar to 500 ps). The proposed LM-MLAA framework can be used for joint reconstruction of activity and attenuation maps from list-mode emission data as standalone or a complementary approach to existing in multimodality imaging such as PET/MRI, where direct measurement attenuation maps is not possible.