Emission computed tomography is an important medical imaging modality in which a radioactive tracer is used to probe anatomical structures or physiological function. The tracer emits gamma rays, which then interact witht he tissues of the body primarily by photoelectric absorption and inelastic Compton scattering. Some of the gamma rays escape the body, pass through a collimator or pinhole aperture and are detected by a device called a gamma-ray camera. This device makes a relatively inaccurate estimate of the position and energy of each gamma ray that strikes it. The objective is to make many such measurements and deduce the three-dimensional distribution of the tracer.

In this talk, we shall discuss some of the analytical and numerical problems that arise in emission tomograpy. We shall present rapid numerical means of modeling the forward problem, an approach to the inverse problem based on a Neumann series, a method for assessing the image quality that can be obtained from a particular data set and a way of optimizing the system for maximum image quality.

This is joint work with Eric Clarkson, Brandon Gallas, Bo Huang, Timothy White, and Anne Clough.

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1996-1997 Mathematics in High Performance Computing