Asymptotic consistency of the maximum likelihood estimate in positron emission tomography and applications. (English) Zbl 0824.62026

Summary: This paper indicates that a minor modification of the maximum likelihood estimate of Y. Vardi, L. A. Shepp and L. Kaufman [J. Am. Stat. 80, 3-37 (1985; Zbl 0561.62094)] can be regarded as a step in the standard nonparametric MLE by the method of sieves and establishes the asymptotic consistency for it. This method of sieves suggests that the number of pixels needs to be in line with the number of detectors in order to avoid poor image reconstructions. A simulation study is also presented to support this suggestion.


62G05 Nonparametric estimation
62P99 Applications of statistics
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
62M99 Inference from stochastic processes


Zbl 0561.62094
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