Time of flight increases noise in MLEM PET reconstructions stopped early: theory, simulations and phantoms

Time of flight (TOF) in positron emission tomography (PET) is expected to greatly reduce image noise, and this can be clearly demonstrated from the likelihood of the problem. Despite this, clinical reconstructions using the maximum likelihood expectation maximization algorithm (MLEM) do not show reduced amounts of noise. In this work we review the theory that predicts the variance of a pixel as a function of iterations in MLEM. We are able to show that when reconstructions are stopped at the earliest iterations, as in clinical setups, TOF increases the noise variance. Nonetheless the convergence of small objects is greatly improved. Therefore, noise reduction can be achieved by performing fewer iterations without loss of image quality. In a second part of this work we perform 2D simulations. The simulations confirm the previous calculations showing a noise increase at the earliest iterations, while the predicted reduction is observed only at full convergence. We also find that the convergence rate of a small sphere improves with timing resolution and becomes more independent of the dimensions of the background object. Without TOF, convergence slows linearly with the background diameter. This can justify the use of less iterations in TOF reconstructions, to achieve equal or better contrast recovery at lower noise compared to traditional MLEM. In the final phase of this work we performed a phantom acquisition on a TOF capable PET scanner. Phantoms with spheres simulating a small or a large background were used. The analysis of the phantoms again showed higher noise with TOF up to about 120 MLEM iterations. The convergence rate of a 15 mm diameter sphere was compared in the small and large configurations and was found to improve using TOF.