Efficient fully 3D list-mode TOF PET image reconstruction using a factorized system matrix with an image domain resolution model

A factorized system matrix utilizing an image domain resolution model is attractive in fully 3D time-of-flight PET image reconstruction using list-mode data. In this paper, we study a factored model based on sparse matrix factorization that is comprised primarily of a simplified geometrical projection matrix and an image blurring matrix. Beside the commonly-used Siddon's ray-tracer, we propose another more simplified geometrical projector based on the Bresenham's ray-tracer which further reduces the computational cost. We discuss in general how to obtain an image blurring matrix associated with a geometrical projector, and provide theoretical analysis that can be used to inspect the efficiency in model factorization. In simulation studies, we investigate the performance of the proposed sparse factorization model in terms of spatial resolution, noise properties and computational cost. The quantitative results reveal that the factorization model can be as efficient as a non-factored model, while its computational cost can be much lower. In addition we conduct Monte Carlo simulations to identify the conditions under which the image resolution model can become more efficient in terms of image contrast recovery. We verify our observations using the provided theoretical analysis. The result offers a general guide to achieve the optimal reconstruction performance based on a sparse factorization model with an image domain resolution model.