Ultra fast 4D PET image reconstruction with user-definable temporal basis functions

Fully 4D image reconstruction, through its use of temporally extensive basis functions, is able to reduce spatiotemporal noise in dynamic PET imaging. This noise reduction has the potential to benefit post-reconstruction kinetic analysis, resulting in improved parametric images. However these benefits come at a significant computational cost: fully 4D reconstruction requires access to the entire time series of fully 3D sinograms (along with the same number of fully 3D scatter and randoms sinogram estimates) in the innermost iterative reconstruction loop. This results in a huge in-memory storage requirement combined with a projection/backprojection workload in the innermost reconstruction loop which is up to 10–40 times greater than conventional static 3D reconstruction (depending on the number of frames). This work presents a practical 4D methodology which i) uses an extremely efficient symmetry & SIMD forward and backprojector for ultra fast computation, ii) compresses the time series of dynamic sinogram data sets without information loss, and iii) permits the use of any user-specified set of temporal basis functions. The result is an extremely fast and flexible fully 4D iterative reconstruction methodology, greatly facilitating the determination of the (perhaps study-specific) optimal temporal basis functions. Whereas single CPU processing for fully 4D list-mode data reconstruction can take in excess of 2 weeks on a single node, the proposed method (using two quad-core CPUs, with span 9 projection data) takes approximately 3.5 hours, giving close to two orders of magnitude acceleration. The method is demonstrated on measured HRRT (High Resolution Research Tomograph) PET data for a [18F]flumazenil study and for an [18F]MPPF study.