Measurement-based spatially-varying point spread function for list-mode PET reconstruction on GPU

We present a novel method to accurately model the spatially-varying point spread function (PSF) of a PET system reformulated for list-mode reconstruction on the graphics processing unit (GPU). The spatially-varying PSF for each LOR is modeled as an asymmetric Gaussian function whose variance changes asymmetrically according to the orientation of the line of response (LOR) and the voxel geometry. To fit the PSF parameters, a point source is imaged at twelve locations in a Philips Gemini TF PET system. To avoid tedious mechanical calibrations, the accurate point source location is estimated directly from the list-mode data. We introduce canonical sinogram to enable reading out the sampled PSF directly from a stack of sinograms by exploring the rotational symmetry of the system matrix. The critical parameters for the PSF model are obtained by solving a convex optimization problem based on the measured point source data. The spatially-varying PSF is efficiently incorporated into the image reconstruction process on the GPU using the CUDA texture memory. The reconstruction algorithm incorporating the measurement-based shift-varying PSF takes 103 milliseconds per iteration to process a million LORs in a 75×75×26 image on a GeForce GTX 480 GPU, which is 190 times faster than a non-PSF implementation on a state-of-the-art central processing unit (CPU), and only 6.8% slower than a spatially-invariant fixed-width Gaussian kernel on the same GPU. Compared with no PSF modeling, this shift-varying PSF shows an average improvement of spatial resolution and contrast to noise ratio for point sources at the periphery of 2.95 ± 0.44% and 159.62 ± 31.54%, respectively. Improvements of the same parameters compared to the spatially-invariant PSF are 1.00 ± 0.26% and 41.11 ± 9.45%, respectively. These results indicate that the fast and accurate spatially-varying PSF reconstruction promises better resolution and contrast recovery with very small additional computational cost.