| Positron emission tomography (PET) is a technique used in medicine to create images of the body that show functionality, not just structure. By using positron-emitting isotopes of elements such as carbon, nitrogen and fluorine to label compounds that play an important role in the metabolism, we can examine the concentrations of these compounds in different tissues. The concentration of the metabolite, and hence the picture of the target organ or structure, is found by counting positron-electron annihilations and processing the data.;PET has been used with much success to identify dead heart tissue in patients who have suffered heart attacks, to identify tumors and measure the success of treatments for removing them in cancer patients, and in other situations where organ function is at issue. Currently, however, the technology does not allow us to pinpoint the exact location of an emission. Instead, each emitted positron annihilates a nearby electron, resulting in a pair of linearly opposed high energy photons. If these photons remain in the plane determined by the ring of detectors that encircles the patient, each photon will be intercepted at one of these detectors, and a count will be recorded for that detector pair. The data are thus the number of emissions found in the tubes between each detector pair.;In this thesis I present a new tree-structured method for constructing a picture of the area of interest from these indirect data. First, a model of the emission process is developed, together with a complementary measure of distortion. The combination allows us to evaluate how well any proposed reconstruction fits the data. Next, the algorithm constructs a progressive series of potential fits to the data by choosing the "best" intensity values for constant intensity image regions, starting with a single region and then making successive tree-structured splits of those regions. Each split allows the program to refine the reconstruction to better approximate the received data. The resulting binary tree describes the regions and intensity values chosen. Finally, a pruning procedure is used to choose the subtree which best models the true underlying distribution of emissions. |
