A comparison of WLS and LS reconstruction for PET

The realizable advantages from statistical reconstruction of positron emission tomography (PET) images remains an unsettled issue. Different iterative reconstruction schemes and convergence effects can lead to different levels of regularization in images. To assess the performance, an analytic approach was used to examine the noise levels of weighted least squares (WLS) and least squares (LS) image reconstruction under the same regularization. For certain non-trivial conditions on the error covariance (weighting) matrix, it was shown that WLS is equivalent to LS reconstruction in a mean square error sense, even when the sinogram noise is not uniform. Also, an approach was proposed for matching the regularization between WLS and LS iterative reconstruction. Computer simulations showed that WLS leads to only a marginally small reduction in noise compared to LS reconstruction at the same resolution