algorithms are developed for estimating statistics for use by parameter estimation algorithms in dynamic tracer studies utilizing positron-emission tomography and requiring high temporal resolution. Two types of stati...
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algorithms are developed for estimating statistics for use by parameter estimation algorithms in dynamic tracer studies utilizing positron-emission tomography and requiring high temporal resolution. Two types of statistics are considered. One can be used with the expectation-maximization algorithm to compute maximum likelihood parameter estimates, and the other computes a histogram of activity levels versus time for use with weighted least squares parameter estimation algorithms. An estimator of the variance of this histogram is also given. Variants for use with both time-of-flight and projection data collected at high frame rates are presented. The algorithms account for the effects of attenuation, randoms, detector efficiency, and nonuniform sampling.
Reconstructions of spatial-distributions of radioactivity produced using maximum-likelihood estimation in positron-emission tomography exhibit noise-like artifacts in the form of sharp peaks and valleys located random...
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Reconstructions of spatial-distributions of radioactivity produced using maximum-likelihood estimation in positron-emission tomography exhibit noise-like artifacts in the form of sharp peaks and valleys located randomly throughout the image field. These become increasingly apparent with each stage of iteration when the expectation-maximization algorithm is used to produce the maximum-likelihood estimate numerically. In this paper, we present a preliminary evaluation of the use of Grenander's method of sieves to reduce these undesirable artifacts.
Let Yij(i=1, …, lii=1, …, J) be independent Poisson random variables, with expectations λ= αiβjiwhere Σαi= l. Such a model is called σ multiplicative Poisson; its factor parameters αi, are called severity fac...
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Let Yij(i=1, …, lii=1, …, J) be independent Poisson random variables, with expectations λ= αiβjiwhere Σαi= l. Such a model is called σ multiplicative Poisson; its factor parameters αi, are called severity factors, and β, are called intensity factors. The article concentrates on the problem of estimating the severity factors αi. Two types of estimators of αiare derived, Bayes and least-squares-maximum-likelihood. The expectations and mean square errors of these estimators are given and their relative efficiency is tabulated. The intensity factors β; are estimated from Ti= Σ Ii=1yij, which are independent and have Poisson distributions with expectations θj= lβj, according to the common procedures.
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