Joint estimation of activity and attenuation in PET/MR using MR-constrained Gaussian priors

Abstract

The maximum likelihood estimation of attenuation and activity (MLAA) has been proposed to jointly estimate activity and attenuation from emission data only. In this paper, we proposed an improved MLAA algorithm by imposing MR spatial and CT statistical constraints on the estimation of attenuation using a constrained Gaussian mixture model (GMM) and a Markov random field (MRF) smoothness prior. We compare the proposed MLAA-GMM algorithm with the MLAA algorithms proposed by Rezaei et al and Salomon et al as well as 4-class MRAC method. Dixon MR images were segmented into outside air, fat and soft tissue classes and an MR low-intensity class corresponding to air cavities, bone and susceptibility artifacts. To eliminate the miss-classification of bones with surrounding tissue, the unknown class was expanded by a co-registered bone probability map. A mixture of 4 Gaussians (air, fat/soft and bone) was used for the unknown class, while unimodal Gaussians were used for others. The algorithms were evaluated using simulation and clinical datasets. The bias in estimated attenuation and activity was evaluated against CT-based attenuation correction. Our results show that MLAA-Rezaei suffers from scale and noise problems. The performance of MLAA-Salomon algorithm is also affected by the scale and depends highly on MR quality and segmentation, especially at air/bone interfaces and vertebra. It was demonstrated the MLAA-GMM effectively exploits MR prior information, thereby results in noise-, crosstalk- and scale-free attenuation maps. The PET bias analyses showed that the MLAA-GMM outperformed the scale corrected MLAA-Rezaei and MLAA-Salomon algorithms as well as the 4-class MRAC method. Therefore, the proposed method can pave the way toward accurate emission-based estimation of attenuation in TOF PET/MR imaging.