AISM 52, 123-138

## Positron emission tomography and random coefficients regression

### Andrey Feuerverger^{1} and Yehuda Vardi^{2}

^{1}Department of Statistics, University of Toronto, 100
St. George St., Toronto, Ontario, Canada M5S 3G3

^{2}Department 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.

**Source**
( TeX , DVI )