CSc 83050

**Discrete Tomography**

Wednesdays 2:00 - 4:00 p.m. - 3 credits - Professor Gabor T. Herman
- ** CODE:
45485
**

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.

** Topics to be Covered:
**

- Discrete Tomography: A Historical Overview
- Sets of Uniqueness and Additivity in Integer Lattices
- Tomographic Equivalence and Switching Operations
- Uniqueness and Complexity in Discrete Tomography
- Reconstruction of Two-Valued Functions and Matrices
- Reconstruction of Connected Sets from Two Projections
- Binary Tomography Using Gibbs Priors
- Probabilistic Modeling of Discrete Images
- Multiscale Bayesian Methods for Discrete Tomography
- Binary Steering of Nonbinary Iterative Algorithms
- 3D Reconstruction from Sparse Radiographic Data
- Heart Chamber Reconstruction from Biplane Angiography
- Discrete Tomography in Electron Microscopy
- Tomography on the 3D-Torus and Crystals

** Textbook for the Course:
**

DISCRETE TOMOGRAPHY:
Foundations, Algorithms and Applications

(Edited by Gabor T. Herman and Attila Kuba)

Birkhauser Boston, 1999