Constrained least squares vs. maximum likelihood reconstructions for Poisson data

Using very small, well-conditioned systems of equations, the performance of least-squares solutions has been compared to the performance of the maximum likelihood solution for Poisson data. It is shown that, at count rates normally encountered in PET (positron emission tomography) or SPECT (single photon emission computed tomography) least-squares methods employing appropriate error weighting perform nearly equivalently to the maximum likelihood method. This suggests that simple schemes for estimating appropriate weights may lead to reconstruction methods having performance equivalent to maximum likelihood using the expectation maximization algorithm but with greatly reduced computation