Fisher Information-Based Evaluation of Image Quality for Time-of-Flight PET

The use of time-of-flight (TOF) information during positron emission tomography (PET) reconstruction has been found to improve the image quality. In this work we quantified this improvement using two existing methods: 1) a very simple analytical expression only valid for a central point in a large uniform disk source and 2) efficient analytical approximations for postfiltered maximum likelihood expectation maximization (MLEM) reconstruction with a fixed target resolution, predicting the image quality in a pixel or in a small region of interest based on the Fisher information matrix. Using this latter method the weighting function for filtered backprojection reconstruction of TOF PET data proposed by C. Watson can be derived. The image quality was investigated at different locations in various software phantoms. Simplified as well as realistic phantoms, measured both with TOF PET systems and with a conventional PET system, were simulated. Since the time resolution of the system is not always accurately known, the effect on the image quality of using an inaccurate kernel during reconstruction was also examined with the Fisher information-based method. First, we confirmed with this method that the variance improvement in the center of a large uniform disk source is proportional to the disk diameter and inversely proportional to the time resolution. Next, image quality improvement was observed in all pixels, but in eccentric and high-count regions the contrast-to-noise ratio (CNR) increased less than in central and low- or medium-count regions. Finally, the CNR was seen to decrease when the time resolution was inaccurately modeled (too narrow or too wide) during reconstruction. Although the maximum CNR is not very sensitive to the time resolution error, using an inaccurate TOF kernel tends to introduce artifacts in the reconstructed image.