A multi-scale stopping criterion for MLEM reconstructions in PET

In this paper we propose and test a new method for terminating the maximum likelihood expectation maximization algorithm for reconstructing positron emission tomography images. The method is based on a stochastic multiresolution analysis which involves all partial sums (scales) of normalized differences between the projected images and the detector data for each row of the sinogram. Previous methods involved only the single total sum of these differences for all detectors. Our method is theoretically founded on recent results from probability theory on the almost sure behaviour of the maximum of the partial sum process for Poisson data. Preliminary tests indicate that this method produces predictions for the optimal stopping iterations which are robust relative to modeling errors in the system matrix and has a signal-to-noise ratio which is 80% of the maximal SNR available from the MLEM iterates.