CSc 83050

**Discrete
Tomography and Its Applications**

Thursdays 2:00 - 4:00 p.m. - 3 credits - Professor
Gabor T. Herman

**Description: **

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.