Parallelizing ray-tracing method for matched conical projector and backprojector in Compton imaging

We propose a new GPU (graphics processing unit)-accelerated method for iterative image reconstruction for Compton imaging, where an exactly matched pair of ray-tracing conical projector and backprojector is parallelized. Unlike the conventional methods including our own previous methods, which use an unmatched pair of ray-tracing forward projector and voxel-based backprojector with approximations, our new method does not involve any approximation in both the forward projection and backprojection operations. To calculate conical forward projection, we accumulate the intersecting chord lengths of the conical rays passing through the voxels using the fast ray-tracing method (RTM). For conical backprojection, to obtain the true adjoint of the conical forward projector, while retaining the computational efficiency of the GPU, we use a voxel-based RTM which is essentially the same as the standard RTM used for the conical forward projector. Our simulation results show that, while the previous methods using unmatched projector-backprojector pairs propagate errors through iterations, our new method is guaranteed to retain the reconstruction accuracy by providing a perfectly matched projector-backprojector pair.