Efficient calculation of resolution and variance in 2-D circular-orbit SPECT

It is useful to be able to predict the statistical properties (resolution and variance) of reconstructions in emission tomography. A general approach to such problems for penalized likelihood reconstruction was proposed in [1], [2], but the direct application of this method is too computationally demanding for practical use. In [3], this general approach was adapted to 2-D PET resulting in practical, efficient ways to calculate statistical properties of reconstructions. However, extending this 2D-PET approach to 2D-SPECT presents challenges due to the nature of attenuation and depth-dependent blur in SPECT. We consider the case of parallel-beam collimated circular-orbit SPECT, and show how the approach in [3] can be extended from PET to SPECT.