On complete-data spaces for PET reconstruction algorithms - Nuclear Science, IEEE Transactions on

As investigators consider more comprehensive measurement models for emission tomography, there will be more choices for the complete-data spaces of the associated expectation-maximization (EM) algorithms for maximumlikelihood (ML) estimation. In this paper, we show that EM algorithms based on smaller complete-data spaces will typically converge faster. We discuss two practical applications of these concepts: (i) the ML-IA and ML-IB image reconstruction algorithms of Politte and Snyder [l] which are based on measurement models that account for attenuation and accidental coincidences in positron-emission tomography (PET), and (ii) the problem of simultaneous estimation of emission and transmission parameters. Although the P E T applications may often violate the necessary regularity conditions, our analysis predicts heuristically that the ML-IB algorithm, which has a smaller complete-data space, should converge faster than ML-IA. This is corroborated by the empirical findings in [l].