A statistical stopping rule 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. It produces both a unique stopping iteration and a set of feasible iterates. The method is based on a stochastic multi-scale analysis which involves partial sums 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 and were unable to produce feasible stopping iterations in the case of modeling errors in the system point spread function. The proposed method (SMAP) is compared with the previous statistical stopping criteria (LV) proposed by Veklerov and Llacer using ensembles of simulated data obtained from a Hoffman brain phantom and a thorax phantom. In these tests, the proposed method produced stopping iterations which were robust relative to modeling errors in the system matrix and improved the signal-to-noise ratio and contrast recovery coefficient of hot regions over the previous LV method.