Statistical behavior of the updating coefficients in the EM algorithm for PET

The authors have studied various convergence properties of the expectation-maximization (EM) algorithm for image reconstruction in positron emission tomography (PET) using simulated projections from the Hoffman phantom. The authors´ main interest was to address the problem of the deterioration of the image quality after a certain number of iterations. More specifically, they have studied the statistical properties of the updating coefficients Δx in the EM algorithm. As a result, they show that the values of the updating coefficients follow a distribution composed of a peak region around 1.0, which includes the pixels in the area of the image where there is non-zero activity, and a tail distribution below 1.0, which corresponds to that part of the image that is far from being completely reconstructed. The authors find that the minimum and average values of the tail is related to the quality of the image and at optimum, as defined by quality criteria, is independent of the number of counts and independent of the shape of the image. The possibility of exploring this property in stopping the algorithm at the optimum image is discussed