Convergence of the block iterative method in image reconstruction for positron emission tomography (PET) requires careful control of relaxation parameters, which is a challenging task. The automatic determination of relaxation parameters for list-mode reconstructions also remains challenging. Therefore, a different approach would be desirable. In this study, we propose a list-mode maximum likelihood Dykstra-like splitting PET reconstruction (LM-MLDS). LM-MLDS converges the list-mode block iterative method by adding the distance from an initial image as a penalty term into an objective function. LM-MLDS takes a two-step approach because its performance depends on the quality of the initial image. The first step uses a uniform image as the initial image, and then the second step uses a reconstructed image after one main iteration as the initial image. In a simulation study, LM-MLDS provided a better tradeoff curve between noise and contrast than the other methods. In a clinical study, LM-MLDS removed the false hotspots at the edge of the axial field of view and improved the image quality of slices covering the top of the head to the cerebellum. List-mode proximal splitting reconstruction is useful not only for optimizing nondifferential functions but also for converging block iterative methods without controlling relaxation parameters.

翻译：正电子发射断层扫描 (PET) 图像重建中，块迭代方法的收敛性要求严格控制松弛参数，这是一项具有挑战性的任务。列表模式重建中松弛参数的自动确定同样困难。因此，需要一种不同的方法。本研究提出一种列表模式最大似然Dykerstra类分裂PET重建方法（LM-MLDS）。LM-MLDS通过在目标函数中添加与初始图像距离的惩罚项，使列表模式块迭代方法收敛。由于LM-MLDS的性能依赖于初始图像质量，该方法采用两步策略：第一步以均匀图像作为初始图像，第二步则使用一次主迭代后的重建图像作为初始图像。仿真研究表明，LM-MLDS在噪声与对比度的权衡曲线上优于其他方法。临床研究表明，LM-MLDS消除了轴向视野边缘的假阳性热点，并改善了覆盖头顶至小脑区域的断层图像质量。列表模式近端分裂重建不仅适用于优化非微分函数，还能在不控制松弛参数的情况下使块迭代方法收敛。