Comparison between three-dimensional positron emission tomography with and without time-of-flight measurement

In positron emission tomography, the time-of-flight measurement improves the signal-to-noise ratio of the reconstructed images. At LETI two three-dimensional analytical reconstruction techniques using this information have been developed. In the present work, they are compared to conventional 3-D convolution-backprojection reconstruction in order to quantify the gain induced by the time-of-flight measurement, as it was done by T. Tomitani (1981) for 2-D reconstruction. The authors establish a formula for the variance of reconstructed images for the three algorithms, and present an analysis of the modulation transfer function