Statistical noise in three-dimensional positron tomography

The authors have derived an approximate expression for the variance at the centre of a uniform spherical source reconstructed using the 3D filtered backprojection technique. The derivation is based on the assumption that the projection data are affected only by Poisson noise, and that the projection is sufficiently finely and uniformly sampled to ensure the validity of the filtered backprojection approach. The expression for the voxel variance in a 3D reconstruction is similar to the usual 2D expression, but contains a factor dependent on the aperture of the cylindrical detector. This factor has been calculated for two different reconstruction filters and in both cases, the influence of the detector aperture on the voxel variance is small. Thus, for an isotropic source such as the uniform sphere, Poisson noise is propagated similarly by both the 2D and 3D filtered backprojection algorithms.