A refined mathematical model for positron emission tomography

The authors introduce a refined version of the mathematical model introduced by Shepp and Vardi (1982) for positron emission tomography. This model replaces the finite-dimensional Shepp-Vardi linear system by a nonstandard integral equation in which the data-space is finite-dimensional, but the unknown emission intensities are represented by a mathematical measure on the region of interest. As in the finite-dimensional model, the authors obtain an iterative procedure which generates a sequence of functions. Such a functional iteration has already been proposed by other researchers for solving a general class of linear inverse problems. However, unlike the finite-dimensional version, to date, the convergence of this infinite-dimensional version has not been established. This paper discusses issues relating to computer data simulation and present examples which suggest that this refined model should eventually lead to more accurate reconstruction algorithms. The authors also present a mathematical approach for proving convergence.