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A statistical model for positron emission tomography. (English) Zbl 0561.62094

Positron emission tomography (PET) - still in its research stages - is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction.

In this article, we tailor a mathematical model to the physics of positron emissions, and we use the model to describe the basic image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data. We describe various estimation procedures, such as the maximum likelihood (ML) method (using the EM algorithm), the method of moments, and the least squares method. A computer simulation of a PET experiment is then used to demonstrate the ML and the least squares reconstructions.

The main purposes of this article are to report on what we believe is an important contribution of statistics to PET and to familiarize statisticians with this exciting field that can benefit from further statistical methodologies to be developed with PET problems in mind. Thus no background in physics or previous knowledge of computerized tomography is assumed. The emphasis is on the basic PET model and the statistical methodology needed for it.


MSC:
62P10Applications of statistics to biology and medical sciences
92C50Medical applications of mathematical biology
62P99Applications of statistics
62N99Survival analysis and censored data