PET statistical image variance with modified LOR acquisition times or efficiencies

It would be possible to design a positron emission tomography scanner to enhance the acquisition durations or efficiencies of certain lines of response (LORs) at the expense of others. In this report we develop the theory of statistical image variance when such weighting is applied, and work out the optimal duration distribution for sequential acquisitions. We further consider a simple example of LOR efficiency modification. The effect of these weighting schemes on image noise variance and relative signal-to-noise ratio (SNR) is evaluated for a clinical example. We find that although global SNR can usually be improved modestly, local SNR may decrease in some regions, and image noise may be less spatially uniform with the weighting than without.