A Statistical Model for Position Emission Tomography: Rejoinder.

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.