Fast projectors for iterative 3D PET reconstruction

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative fully 3D image reconstruction. The fast projector pair is used as part of a factored system matrix that models detector-pair response with a shift variant sinogram blur kernel. In this way we are able to combine the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector uses the exact inverse rebinning equation to map stacked 2D transaxial projections into a full 3D sinogram. The back projector is simply the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LOR). The inverse rebinning projector differs in performance by less than 1% in RMS error from the fully 3D geometric projector computed using solid angle calculations of voxel-wise sensitivity along each LOR. The cost of forward and back projection for the microPET Focus220 small animal scanner using the inverse rebinning projector is 5 to 15 times less than that for the fully 3D geometric projector, depending on the reconstructed field of view and voxel size. We compare performance between the inverse rebinning and 3D geometric projectors using simulated point and phantom data and in vivo FDG mouse data.