Students will learn about and research a practical problem in limited data tomography (when some data are missing). We will focus on Compton Scattering Tomography, Sonar, and Seismic Imaging, three important types of limited data problems. Students will first learn about the field and then program an algorithm for a specific problem. Students will test and evaluate the performance of the algorithm. Typically, reconstructions (pictures of objects) from limited data show only some parts of the object and produce artifacts. By looking at the reconstructions and how the data are collected, students will conjecture what the artifacts are and why they appear and then work to improve the algorithm. The students will use novel data acquisition methods to determine whether there are new artifacts that have not been categorized. Depending on the student’s background, we might discuss the mathematics that explains the visible singularities and artifacts.
Desired Background: Calculus plus some knowledge of Matlab or a high-level computer language.