Joint Estimation of Activity and Attenuation in Whole-Body TOF PET/MRI Using Constrained Gaussian Mixture Models

It has recently been shown that the attenuation map can be estimated from time-of-flight (TOF) PET emission data using joint maximum likelihood reconstruction of attenuation and activity (MLAA). In this work, we propose a novel MRI-guided MLAA algorithm for emission-based attenuation correction in whole-body PET/MR imaging. The algorithm imposes MR spatial and CT statistical constraints on the MLAA estimation of attenuation maps using a constrained Gaussian mixture model (GMM) and a Markov random field smoothness prior. Dixon water and fat MR images were segmented into outside air, lung, fat and soft-tissue classes and an MR low-intensity (unknown) class corresponding to air cavities, cortical bone and susceptibility artifacts. The attenuation coefficients over the unknown class were estimated using a mixture of four Gaussians, and those over the known tissue classes using unimodal Gaussians, parameterized over a patient population. To eliminate misclassification of spongy bones with surrounding tissues, and thus include them in the unknown class, we heuristically suppressed fat in water images and also used a co-registered bone probability map. The proposed MLAA-GMM algorithm was compared with the MLAA algorithms proposed by Rezaei and Salomon using simulation and clinical studies with two different tracer distributions. The results showed that our proposed algorithm outperforms its counterparts in suppressing the cross-talk and scaling problems of activity and attenuation and thus produces PET images of improved quantitative accuracy. It can be concluded that the proposed algorithm effectively exploits the MR information and can pave the way toward accurate emission-based attenuation correction in TOF PET/MRI.