To improve robustness and accuracy of MR-based PET attenuation correction for PET/MR.The emerging hybrid PET/MR imaging modality provides great promise in a number of clinical applications.¹ PET attenuation correction is critical to accurate PET quantitation. The most commonly used MR-segmentation based PET attenuation correction approach has challenges in implants, bones, lungs and internal air cavities, which are difficult to distinguish in MR. An alternative approach is based on joint estimation (JE)² of PET attenuation and activity using PET emission scan data. Although the inverse problem for JE is highly ill-conditioned, PET time-of-flight (TOF) information greatly improves the conditioning and reduces crosstalk artifacts.³ Those two segmentation-based and JE-based approaches have been combined into selective update JE⁴ where PET attenuation values are calculated by JE selectively in MR-dark regions and otherwise determined by the MR-segmentation based method. In this work, a more general JE approach with MR-based priors⁵ is developed where MR-based prior weights can be spatially modulated to locally control the degree of weights given to JE or MR-segmentation. The JE algorithm with MR-based priors was evaluated on TOF PET/MR clinical data.Patients were scanned on a GE Signa PET/MR scanner (GE Healthcare, Waukesha, WI, USA) with TOF timing resolution of <400 ps. For each patient, a dedicated 3D GRE scan (FA=5°) with Dixon-type fat-water separation and a whole-body FDG TOF PET emission scan were acquired. An MR-based attenuation map was obtained using 4-class MR-segmentation (water, fat, lung and air) as described by Wollenweber et al.⁶ where a TOF OSEM (ordered subsets expectation maximization)⁷ image was used for completing truncated regions in MR. The MR-based attenuation map was taken as an MR-based prior map for JE. To differentiate between reliable soft-tissue MR signals and uncertain low MR signal regions, a threshold was derived, based on two level Huang threshold method, from MR histogram distributions, as in Cheng et al.⁴ An MR-based prior weight map was generated by assigning low weights to the uncertain low MR signal regions and high weights to the other regions. Given the TOF PET emission scan data, an attenuation map and an activity image are jointly reconstructed by maximizing the following objective function: $$\Phi(\mu,\lambda)=L(\mu,\lambda)-R^{\rm{MR}}(\mu)-R^{\rm{smoothing}}(\mu)$$where $$$\lambda$$$ and $$$\mu$$$ represent the activity image and the attenuation map to estimate, respectively. In the objective function, $$$L(\mu,\lambda)$$$ is the Poisson log-likelihood function for the TOF PET emission data; $$$R^{\rm{MR}}(\mu)=\sum_j \beta_j (\mu-\mu^{\rm{MR}})^2$$$ is the MR-based prior where $$$\beta_j$$$ are voxel-wise MR-based prior weights and $$$\mu^{\rm{MR}}$$$ is the MR-based prior map; and $$$R^{\rm{smoothing}}(\mu)=\beta^{\rm{smoothing}} \sum_j \sum_{k\in N_j}w_{jk} (\mu_j-\mu_k)^2$$$ is the quadratic smoothing penalty where $$$\beta^{\rm{smoothing}}$$$ is a smoothing parameter, $$$w_{jk}$$$ are predetermined weights and $$$N_j$$$ is the set of neighborhoods of voxel $$$j$$$. The attenuation map $$$\mu$$$ and the activity image $$$\lambda$$$ were alternatively updated where OSTR (ordered subset transmission)⁸ was used for updating $$$\mu$$$ and TOF OSEM⁷ for updating $$$\lambda$$$.Figs. 1 and 2 show representative coronal slices from the results. Fig. 1(a) shows an MR in-phase image with a dark region due to a hip implant, and Fig. 1(b) shows the MR-based attenuation map with the implant-induced artifact. Fig. 1(c) shows the attenuation map obtained using the JE algorithm with MR-based priors. Fig. 1(c) shows the attenuation of the hip implant is recovered by JE. In addition, the lung boundary in the JE-based attenuation map seems more accurate that that in the MR-based attenuation map in the sense that the lung boundary in Fig. 1(c) is closer to that in Fig. 1(a) than that in Fig. 1(b) is. Figs. 1(d) and (e) are TOF OSEM activity images reconstructed with the MR-based and the JE-based attenuation maps, respectively. Similarly, Fig. 2 shows, for a different slice, the MR in-phase image (Fig. 2(a)), the MR-based attenuation map (Fig. 2(b)), the JE-based attenuation map (Fig. 2(c)) and TOF OSEM images reconstructed using the MR-based and the JE-based attenuation maps in Figs. 2(d) and (e), respectively. The JE-based attenuation map shows the metal pins are recovered (Fig. 2(c)) whereas the metal pins generate artifacts in the MR image (Fig. 2(a)) and the MR-based attenuation map (Fig. 2(b)).A joint estimation algorithm with MR-based priors is developed to improve MR-segmentation based attenuation correction. The JE algorithm with MR-based priors was applied to whole-body TOF PET/MR clinical data and it was demonstrated that the JE algorithm can recover the attenuation of implants, greatly improving robustness and accuracy of MR-based attenuation correction. Here TOF information is critical to the success of JE.