A pseudo-Poisson noise model for simulation of positron emission tomographic projection data

Although radioactive decay obeys Poisson statistics, because of the corrections that are applied to the projection data prior to reconstruction, the noise in positron emission tomography (PET) projections does not follow a Poisson distribution. Use of Poisson noise when simulating PET projections in order to test the performance of reconstruction and processing techniques is therefore not appropriate. The magnitude of PET projection noise was observed to be as much as 10 to 100 times greater than Poisson noise in some instances. A quadratic function was found to fit the relationship between noise power spectral density and total projection count. The coefficients of the quadratic function were determined for projections of different tracer distributions and types. Using these observations, a method of simulating PET projections was developed based on a pseudo-Poisson noise model. Projections simulated according to this method are good approximations to real projection data and take into account the characteristics of individual PET cameras and particular tracer distributions. Such simulated projections have been valuable in predicting the performance of reconstruction algorithms. This approach can also be applied to single photon emission tomography.