Overview

In positron emission tomography (PET) and single photon emission tomography (SPECT), the patient inhales or is injected with chemicals to which radioactive material has been chemically attached [187]. The chemicals are designed to accumulate in that specific region of the body we wish to image. For example, we may be looking for tumors in the abdomen, weakness in the heart wall, or evidence of brain activity in a selected region. The patient is placed on a table surrounded by detectors that count the number of emitted photons. On the basis of where the various counts were obtained, we wish to determine the concentration of radioactivity at various locations throughout the region of interest within the patient.

In SPECT the radionuclide emits single photons, which then travel through the body of the patient and, in some fraction of the cases, are detected. Detections in SPECT correspond to individual sensor locations outside the body. The data is SPECT are the photon counts at each of the finitely many detector locations.

In PET the situation is different. The radionuclide emits individual positrons, which travel, on average, between 4 mm and 2 .5 cm (depending on their kinetic energy) before encountering an electron. The resulting annihilation releases two gamma-ray photons that then proceed in essentially opposite directions. Detection in the PET case means the recording of two photons at nearly the same time at two different detectors. The locations of these two detectors then provide the end points of the line segment...