Tomography and Its Applications
Thursdays 2:00 - 4:00 p.m. - 3 credits - Professor Gabor T. Herman
We assume that there is a domain, which may itself be discrete (such as a set of ordered pairs of integers) or continuous (such as Euclidean space). We further assume that there is an unknown function f whose range is known to be a given discrete set (usually of real numbers). The problems of discrete tomography have to do with determining f (perhaps only partially, perhaps only approximately) from weighted sums over subsets of its domain in the discrete case and from weighted integrals over subspaces of its domain in the continuous case. In many applications these sums or integrals may be known only approximately. From this point of view, the most essential aspect of discrete tomography is that knowing the discrete range of f may allow us to determine its value at points where without this knowledge it could not be determined. Discrete tomography is full of mathematically fascinating questions and it has many interesting applications. In this course we will be concentrating on the computer algorithms that have been developed to solve problems of discrete tomography and the applications of these algorithms in fields such as electron microscopy, materials science, non-destructive testing, diagnostic radiology, and geological exploration.