GPU-Based PET Image Reconstruction Using an Accurate Geometrical System Model

In positron emission tomography (PET), 3D iterative image reconstruction methods have a huge computational burden. In this paper, we developed a list-mode image reconstruction method using graphics processing units (GPUs). Efficiency of acceleration for GPU implementation largely depends on the method chosen, where a reduced number of conditional statements and a reduced memory size are required. On the other hand, accurate system models are required to improve the quality of reconstructed images. Various accurate system models for conventional CPU implementation have been proposed, but these models basically require many conditional statements and huge memory size. Therefore, we developed a new system model which matches GPU implementation better. In this model, the detector response functions, which vary depending on each line of response (LOR), are pre-computed in CPUs and modeled by sixth-order polynomial functions in order to reduce the memory size occupied in GPUs. Each element of a system matrix is obtained on-the-fly in GPUs by calculating the distance between an LOR and a voxel. Therefore the developed system model enables efficient GPU implementation of the accurate system modeling with a reduced number of conditional statements and a reduced memory size. We applied the developed method to a small OpenPET prototype, in which 4-layered depth-of-interaction (DOI) detectors were used. For image reconstruction, we used the dynamic row-action maximum likelihood algorithm (DRAMA). Compared with a conventional model for GPU implementation, in which DRFs are given as a Gaussian function of fixed width, we saw no remarkable difference for DOI data, but for non-DOI data the proposed model outperformed the conventional at the peripheral region of the field-of-view. The proposed model had almost the same calculation time as the conventional model did. For further acceleration, we tried parallel GPU implementation, and we obtained 3.8-fold acceleration by using 4 GPUs.