People who are interested in PET-MRI research Joint reconstruction of PET and MRI is aimed to improve both PET and MR image quality using information from each other’s imaging modality. However, the aim cannot be achieved without correcting the attenuation of PET, which is one of the most significant factors that affect image quality and quantitative accuracy. In our work, we proposed a method to correct attenuation during the process of simultaneous PET and MRI images reconstruction. This method integrates PET, MRI and TOF information, which is named as Joint Reconstruction of Activity, Attenuation and MRI (JRAAM). A 2-D simulation experiment was implemented to evaluate the performance of the proposed method.

Algorithm: Based on the work of Ehrhardt about PET-MRI joint reconstruction (JR) [1], which reconstructs PET and MRI images at the same time, we integrated the information of TOF and the idea of Maximum likelihood activity and attenuation (MLAA) [2] into the joint reconstruction to correct attenuation. Thus, in the proposed method, the joint objective function of PET (u) and MRI (v) is modified as: $$J(u,v)=\sum_{it}(\sum_jC_{ijt}u_{j}-y_{it}\log_{}({\sum_j}C_{ijt}u_{j}))+\frac{1}{2\sigma^{2}}{\mid Bv-g\mid }^{2}+\alpha R(u,v)\cdot\cdot\cdot\cdot\cdot\cdot (1)$$

Where C, B and R represent PET system matrix, MRI system matrix and prior knowledge, respectively. Moreover, y is sinogram counts in each LOR and g is acquired MRI data. R is joint total variation, which is defined as:$$R(u,v)=\int_{Ω}^{}({\mid \triangledown u \mid}^{2}+{\mid \triangledown u \mid}^{2}+\beta^{2})^{\frac{1}{2}} \cdot\cdot\cdot\cdot\cdot\cdot(2)$$

Where β is a smooth entry whose value needs adjusting.

To minimize the objective function (Eq.1), a quasi-Newton method named L-BFGS-B [3] is exploited. After L-BFGS-B iteration, the PET images and MRI images are updated. Next step, the attenuation coefficient distribution is updated through the maximum likelihood for transmission tomography (MLTR) algorithm. Then those updated PET, MRI and attenuation data are applied to next iteration cycle. The whole process is presented as Fig.1.

Simulation experiment: To evaluate the proposed method, a NCAT phantom was used with only one slice due to the concern of computation time. Emission data from PET scanner was simulated by GATE [4], in which a simulated Siemens Biograph mMR system was constructed. The TOF information was obtained by simulation on MATLAB and MRI images were acquired from a MRI simulation software MRILAB [5]. Then, the JRAAM algorithm was implemented on MATLAB. The weights of PET and MRI entries determine which one of these two images is dominated and affect the reconstructed image quality. Therefore, the objective function was rewritten as: $$J(u,v)=\gamma_{1}(\sum_{it}(\sum_jC_{ijt}u_{j}-y_{it}\log_{}({\sum_j}C_{ijt}u_{j})))+\gamma_{2}(\frac{1}{2\sigma^{2}}{\mid Bv-g\mid }^{2})+\alpha R(u,v)\cdot\cdot\cdot\cdot\cdot\cdot (3)$$

Where γ₁ and γ₂ represent the weight of PET and MRI entry, respectively. Finally, the reconstruction results were compared with MLEM and MLAA.

Reconstructed MLEM, MLAA and JRAAM images of the simulation phantom are shown in Fig.2. The variances in two uniform regions of interest (ROI), which represent noise level, are calculated in Tab.1. Besides, the two line plots that cross myocardium and tumor are presented in Fig.3 and Fig.4, respectively. These results illustrate that JRAAM performs better in decreasing noise and revealing myocardium and tumor compared with MLAA. However, JRAAM indicates a little bit higher noise bias than the reference MLEM results where no attenuation correction is introduced. The use of TOF in attenuation correction might result in noise bias. However, incorporating MR information in the joint reconstruction (JRAAM), the errors brought by TOF could be reduced. We have proposed a new method to correct attenuation in PET-MRI joint reconstruction and validated its feasibility by the simulated phantom. In further study, JRAAM should be extended to 3D phantom and even be applied in clinical data.