On complete-data spaces for PET reconstruction algorithms

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 maximum-likelihood (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 [1] 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 PET 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 [1].