Abstract
The local noise property of a 3D PET reconstructed image is investigated for a uniform-activity sphere distributed in a constantly attenuating spherical object. The positional dependence of the statistical noise is approximately derived and calculated for some special cases. It is suggested that a larger diameter of the activity sphere causes noise amplification, and the noise property for the large attenuating sphere is close to that for a non-attenuating object with the same total number of measuring counts. By considering noise propagation of two spherical activity distributions, we suggest that the signal-to-noise ratio of the image depends on a set of projection directions and the sizes and intensities of the activity distributions. In a simple case, we derive an optimal value of the maximum acceptance angle for the projection directions to improve the signal-to-noise ratio of the image.
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