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The article presents a rejoinder to comments made on their article "A Statistical Model for Position Emission Tomography." Being a very active, multidisciplinary, field of research, it is hard to keep track of who suggested what and in what context, so in attempting to answer scholar Donald B. Rubin's question we are likely to overlook some contributors. The first use of a pixel model for an organ appeared in scholar G.N. Hounsfield's original development of X-ray computerized tomography. In 1978 scholars gave a short account of this early development in the field, including images produced using Hounsfield's algorithms. The fact that the physics of Position Emission Tomography (PET) is different, and inherently more stochastic, than that of X-ray transmission tomography has been common knowledge. Realizing that the additional randomness of PET calls for a more statistical way of thinking, scholars A.J. Rockmore and A.Macovski suggested estimating the emission density in PET, using a maximum-likelihood approach. Their paper fell short of identifying the connection between the tube count and the emission density. This omission on their part is probably a result of being unaware of the development of statistical methods for incomplete data.

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. [ABSTRACT FROM AUTHOR]