List-Mode PET Image Reconstruction Using Dykstra-Like Splitting

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.