POSITRON EMISSION TOMOGRAPHY AND RANDOM COEFFICIENTS REGRESSION

ANDREY FEUERVERGER^{1}* AND YEHUDA VARDI^{2}**

1Department of Statistics, University of Toronto, 100 St. George St., Toronto, Ontario, Canada M5S 3G3 2Department of Statistics, Rutgers University, 110 Frelinghuysen Rd. Piscataway, NJ 08854-8019, U.S.A.

(Received December 15, 1997; revised August 3, 1998)

Abstract. We further explore the relation between random coefficients regression (RCR) and computerized tomography. Recently, Beran et al. (1996, Ann. Statist., 24, 2569–2592) explored this connection to derive an estimation method for the nonparametric RCR problem which is closely related to image reconstruction methods in X-ray computerized tomography. In this paper we emphasize the close connection of the RCR problem with positron emission tomography (PET). Specifically, we show that the RCR problem can be viewed as an idealized (continuous) version of a PET experiment, by demonstrating that the nonparametric likelihood of the RCR problem is equivalent to that of a specific PET experiment. Consequently, methods independently developed for either of the two problems can be adapted from one problem to the other. To demonstrate the close relation between the two problems we use the estimation method of Beran, Feuerverger and Hall for image reconstruction in PET.

Key words and phrases: Computerized tomography, fast Fourier transform, nonparametric likelihood, positron emission tomography, projection-slice theorem, Radon transform, random coefficients regression, regularization, smoothed EM algorithm.