DISCRETE TOMOGRAPHY WORKSHOP

25-27 August, 1997
Szeged, Hungary

Supported by the Hungarian Academy of Sciences, Hungary, and
the National Science Foundation, USA

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, as we perceive the field, 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.

Participants:


USA



Hungary



Others:



Organisers:



The Workshop will take place in the Hotel Forras
Address: H-6726 Szeged, Szent-Gyorgyi Albert u. 16-24, Szeged, Hungary,
Phone: +36-62-430-130,
Fax: +36-62-430-130/500
Previous meeting:

DIMACS Mini-Symposium on Discrete Tomography

September 19, 1994
DIMACS
Rutgers University

DIMACS sponsored a one-day mini symposium on discrete tomography. In continuous tomography, a density f(x,y) is to be reconstructed from its integrals over lines or sub-manifolds. In discrete tomography, the "density" is either 1 or 0 at each point of a lattice and represents the presence or absence of an atom at the site. Line integrals are now line sums. Thus, if S is a finite subset of the lattice E = Z2 or Z3, and if D is a finite set of (main) directions in E, we measure the line sums of S along every line with a direction in D. When is S uniquely determined? How large does D have to be to determine every convex set S which is confined to a given box? How large does a box have to be before uniqueness fails for convex sets? Problems of this general type, which arise in transmission electron microscopy of crystals, will be discussed. Related problems in geometric and in continuous tomography will also be discussed. A tour of a lab in Holmdel which measures the above line sums for a given crystal, S, using a transmission electron microscope will be arranged for interested participants.