List-Mode PET Image Reconstruction Using Dykstra-Like Splitting

To converge the block iterative method in image reconstruction for positron emission tomography (PET), careful control of relaxation parameters is required, which is a challenging task. The automatic determination of relaxation parameters for list-mode reconstructions also remains challenging. Therefore, a different approach than controlling relaxation parameters would be desired by list-mode PET reconstruction. 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. We evaluated LM-MLDS using simulation and clinical data. LM-MLDS provided a higher peak signal-to-noise ratio and suppressed an oscillation of tradeoff curves between noise and contrast than the other block iterative 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. LM-MLDS showed different noise properties than the other methods due to Gaussian denoising induced by the proximity operator. The list-mode proximal splitting PET reconstruction is useful not only for optimizing nondifferentiable functions such as total variation but also for converging block iterative methods without controlling relaxation parameters.