Fast and memory-efficient reconstruction of sparse Poisson data in listmode with non-smooth priors with application to time-of-flight PET.

Objective.Complete time of flight (TOF) sinograms of state-of-the-art TOF PET scanners have a large memory footprint. Currently, they contain ∼4 · 109data bins which amount to ∼17 GB in 32 bit floating point precision. Moreover, their size will continue to increase with advances in the achievable detector TOF resolution and increases in the axial field of view. Using iterative algorithms to reconstruct such enormous TOF sinograms becomes increasingly challenging due to the memory requirements and the computation time needed to evaluate the forward model for every data bin. This is especially true for more advanced optimization algorithms such as the stochastic primal-dual hybrid gradient (SPDHG) algorithm which allows for the use of non-smooth priors for regularization using subsets with guaranteed convergence. SPDHG requires the storage of additional sinograms in memory, which severely limits its application to data sets from state-of-the-art TOF PET systems using conventional computing hardware.Approach.Motivated by the generally sparse nature of the TOF sinograms, we propose and analyze a new listmode (LM) extension of the SPDHG algorithm for image reconstruction of sparse data following a Poisson distribution. The new algorithm is evaluated based on realistic 2D and 3D simulationsn, and a real data set acquired on a state-of-the-art TOF PET/CT system. The performance of the newly proposed LM SPDHG algorithm is compared against the conventional sinogram SPDHG and the listmode EM-TV algorithm.Main results.We show that the speed of convergence of the proposed LM-SPDHG is equivalent the original SPDHG operating on binned data (TOF sinograms). However, we find that for a TOF PET system with 400 ps TOF resolution and 25 cm axial FOV, the proposed LM-SPDHG reduces the required memory from approximately 56 to 0.7 GB for a short dynamic frame with 107prompt coincidences and to 12.4 GB for a long static acquisition with 5·108prompt coincidences.Significance.In contrast to SPDHG, the reduced memory requirements of LM-SPDHG enables a pure GPU implementation on state-of-the-art GPUs-avoiding memory transfers between host and GPU-which will substantially accelerate reconstruction times. This in turn will allow the application of LM-SPDHG in routine clinical practice where short reconstruction times are crucial.