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 algorithms for maximum-likelihood estimation. It is shown that EM algorithms based on smaller complete-data spaces will typically converge faster. Two practical applications of these concepts are discussed: the ML-IA and ML-IB image reconstruction algorithms of D.G. Politte and D.L. Snyder (1991) which are based on measurement models that account for attenuation and accidental coincidences in positron emission tomography (PET); and the problem of simultaneous estimation of emission and transmission parameters. Although the PET applications may often violate the necessary regularity conditions, the authors´ analysis predicts heuristically that the ML-IB algorithm, which has a smaller complete-data space, should converge faster than ML-IA