Gabor T. Herman 
Attila Kuba

Lajos Rodek

The meeting took
place at the The Graduate Center
of
the City University of New York
(365 Fifth Avenue, New York,
NY 10016, USA, on the opposing corner from the Empire State Building)
in the wellequiped and beautifully appointed
Elebash
Recital Hall.
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.
Further details can be obtained by
looking at
DISCRETE
TOMOGRAPHY: Foundations, Algorithms and Applications
(Edited by Gabor T. Herman and Attila Kuba)
Birkhäuser Boston, 1999
The workshop reception was held in the Lobby of the Elebash Recital Hall on June 13 between 6:00 PM  7:00 PM.
There was an optional
conference dinner on June 14
from 7:00 PM in the razil
Brazil Churrascaria at the cost
of $75 per person, including drinks..
June 13
registration and opening (9:30  10:00)
Foundations of DT I.
10:00  10:30

1. Gardner: Discrete Point XRays of
Convex Lattice Sets

10:30  11:00

2. Hajdu: Unique Reconstruction of
Bounded Sets in Discrete Tomography

Foundations of DT II.
11:30  12:00

3. Kaneko: Structure of Total
Reconstructed Sets from Given Two Projection Data

12:00  12:30

4. Zopf: Reconstruction of Measurable
Sets from Two Generalized Projections

12:30  1:00

5. Daurat: Determination of Qconvex
Bodies by XRays

Foundations of DT III.
2:00  2:30

6. Dahl: Matrices of Zeros and Ones with
Given Line Sums and a Zero Block

2:30  3:00

7. Picouleau: Reconstructing a Binary
Matrix under Timetabling Constraints

3:00  3:30

8. Vallejo: Minimal Matrices and Discrete
Tomography

Connections of DT with Other Mathematical Fields I.
4:00  4:30

9. D'Ariano: Quantum Tomography for
Imaging

4:30  5:00

10. Grassl: Tomography of Quantum States
in Small Dimensions

5:00  5:30

11. Roetteler: Solution to the Mean
King's Problem in Prime Power Dimensions using Discrete Tomography

5:30  6:00

12. Huck/Langfeld: Discrete Tomography of
Mathematical Quasicrystals: A Primer

Connections of DT with Other Mathematical Fields II.
9:30  10:00

13. Severini: On the Xrays of
Permutations

10:00  10:30

14. Kazantsev: Optimal Ordering of
Projections using Permutation Matrices and Angles between Projection
Subspaces

10:30  11:00

15. Imiya: Tomography on Finite Graphs

DT Reconstruction Algorithms I.
11:30  12:00

16. Brimkov: Exact Image Reconstruction
from a Single Projection through Real Computation

12:00  12:30

17. Batenburg: A New Algorithm for 3D
Binary Tomography

12:30  1:00

18. Capricelli: Parallel BlockIterative
Reconstruction Algorithms for Binary Tomography

DT Reconstruction Algorithms II.
2:00  2:30

19. Costa: Reconstruction of Binary
Matrices under Adjacency Constraints

2:30  3:00

20. Ruskó: MultiResolution Method
for Binary Tomography

3:00  3:30

21. Weber: Prior Learning and
ConvexConcave Regularization of Binary Tomography

DT Reconstruction Algorithms III.
4:00  4:30

22. Balázs: Reconstruction of
Discrete Sets from Four Projections: Strong Decomposability

4:30  5:00

23. Kuba: An Efficient Algorithm for
Reconstructing Binary Matrices from Horizontal and Vertical Absorbed
Projections

5:00  5:30

24. Schüle: Adaptive Reconstruction
of DiscreteValued Objects from Few Projections

5:30  6:00

25. Kiss: DIRECT: DIscrete REConstruction
Techniques

Applications of DT I.
9:30  10:00

26. Liao: Discrete Tomography with a Very
Few Views, using Gibbs Priors and a Marginal Posterior Mode Approach

10:00  10:30

27. Alpers: Resolving Ambiguities in
Reconstructed Grain Maps using Discrete Tomography

10:30  11:00

28. Herman: Discrete Tomographic
Reconstruction of 2D Polycrystal Orientation Maps From XRay
Diffraction Projections Using Gibbs Priors

Applications of DT II.
11:30  12:00

29. Krimmel: Discrete Tomography for
Reconstruction from Limited View Angles in NonDestructive Testing

12:00  12:30

30. Rodek: Reconstruction of PixelBased
and Geometric Objects by Discrete Tomography. Simulation and Physical
Experiments

12:30  1:00

31. Schillinger: Proposed Combination of
CAD Data and Discrete Tomography for the Detection of Coking and
Lubricants in Turbine Blades or Engines

Applications of DT III.
2:00  2:30

32. Gérard: Application of a
Discrete Tomography Algorithm to Computerized Tomography

2:30  3:00

33. Nagy, A.: Reconstruction of Factor
Structures using Discrete Tomography Method

3:00  3:30

34. Zdunek: Detection of Subsurface
Bubbles with Discrete Electromagnetic Geotomography

Connections of DT with Other Mathematical Fields III.
4:00  4:30

35. Sharif: Discrete Tomography in
Discrete Deconvolution: Deconvolution of Binary Images using Ryser's
Algorithm

4:30  5:00

36. Nagy, B.: An Algorithm to Find the
Number of the Digitizations of Discs with a Fixed Radius

5:00  5:30

37. Servières: The Mojette
Transform: Discrete Angles for Tomography

Special session after the closing (science in action, as captured by Barbara Langfeld)
Name 
University/Company 
Town 
Country 
A. Alpers 
Cornell Univ. 
Ithaca, NY 
USA 
P. Balázs 
Univ. Szeged 
Szeged 
Hungary 
R.P. Barneva 
State Univ. New York 
Fredonia, NY 
USA 
K.J. Batenburg 
Leiden Univ. 
Leiden 
The Netherlands 
V.E. Brimkov 
Fairmont State University 
Fairmont, WV 
USA 
L.G. Butler 
Louisiana State Univ. 
Baton Rouge, LA 
USA 
T.D. Capricelli 
Univ. Paris 6 
Paris 
France 
L. Cavalier 
Univ. Provence 
Marseille 
France 
M.T. Chan 
GE Global Research 
Niskayuna, NY 
USA 
W. Chen 
Grad. Center, CUNY 
New York, NY 
USA 
P.L. Combettes 
Univ. Paris 6 
Paris 
France 
M.C. Costa 
CedricCNAM 
Paris 
France 
G. Dahl 
Univ. Oslo 
Oslo 
Norway 
G.M. D'Ariano 
Univ. Pavia 
Pavia 
Italy 
A. Daurat 
Univ. Strasbourg 
Strasbourg 
France 
R. Davidi 
Grad. Center, CUNY 
New York, NY 
USA 
J. Dubowy 
Grad. Center, CUNY 
New York, NY 
USA 
R.J. Gardner 
Western Washington Univ. 
Bellingham, WA 
USA 
E. Garduno 
Univ. of California 
San Diego, CA 
USA 
Y. Gerard 
Univ. Auvergne 
Aubiere 
France 
M. Grassl 
Univ. Karlsruhe 
Karlsruhe 
Germany 
L. Hajdu 
Univ. Debrecen 
Debrecen 
Hungary 
G.T. Herman 
Grad. Center, CUNY 
New York, NY 
USA 
C. Huck 
Univ. Bielefeld 
Bielefeld 
Germany 
A. Imiya 
Chiba Univ. 
Chiba 
Japan 
A. Jain 
Johns Hopkins Univ. 
Baltimore, MD 
USA 
A. Kaneko 
Ochanomizu Univ. 
Tokyo 
Japan 
I. Kazantsev 
Univ. Pennsylvania 
Philadelphia, PA 
USA 
Z. Kiss 
Univ. Szeged 
Szeged 
Hungary 
A. Klappenecker 
Texas A&M Univ. 
College Station, TX 
USA 
E. Knudsen 
Riso Natl. Lab. 
Roskilde 
Denmark 
K. Koto 
Ochanomizu Univ. 
Tokyo 
Japan 
S. Krimmel 
Technical Univ. of Munich/Siemens AG 
GarchingMunich 
Germany 
A. Kuba 
Univ. Szeged 
Szeged 
Hungary 
B. Langfeld 
Techn. Univ. of Munich 
GarchingMunich 
Germany 
H. Liao 
Grad. Center, CUNY 
New York, NY 
USA 
K. Lord 
Techn. Univ. of Munich 
GarchingMunich 
Germany 
R. Luke 
Univ. Delaware 
Newark, DE 
USA 
S. Matej 
Univ. of Pennsylvania 
Philadelphia, PA 
USA 
K. Mueller 
Stony Brook Univ. 
Stony Brook, NY 
USA 
R. Nagahama 
Ochanomizu Univ. 
Tokyo 
Japan 
A. Nagy 
Univ. Szeged 
Szeged 
Hungary 
B. Nagy 
Univ. Debrecen 
Debrecen 
Hungary 
C. Picouleau 
CedricCNAM 
Paris 
France 
H.F. Poulsen 
Riso Natl. Lab. 
Roskilde 
Denmark 
C.V.S. Rao 
Inst. Plasma Research 
Bhat, Gandhinagar 
India 
L. Rodek 
Grad. Center, CUNY 
New York, NY 
USA 
M. Roetteler 
NEC Laboratories America, Inc. 
Princeton, NJ 
USA 
S. Rowland 
Grad. Center, CUNY 
New York, NY 
USA 
L. Ruskó 
Univ. Szeged 
Szeged 
Hungary 
M. Santoyo Mondragón 
Univ. Mich. de San Nicolás de Hidalgo 
Morelia, Michoacán 
Mexico 
D. Sarioz 
Grad. Center, CUNY 
New York, NY 
USA 
B. Schillinger 
Techn. Univ. of Munich 
GarchingMunich 
Germany 
C. Schnörr 
Univ. Mannheim 
Mannheim 
Germany 
T. Schüle 
Univ. Mannheim 
Mannheim 
Germany 
M. Servières 
Univ. Nantes 
Nantes 
France 
S. Severini 
Univ. York 
York 
U.K. 
B. Sharif 
Univ. Illinois 
Urbana, IL 
USA 
M. Tajine 
Univ. Strasbourg 
Strasbourg 
France 
E. Vallejo 
Univ. Nac. Autónoma de México 
Morelia, Michoacán 
Mexico 
E. VardiGonen 
Grad. Center, CUNY 
New York, NY 
USA 
S. Weber 
Univ. Mannheim 
Mannheim 
Germany 
C.E. Yarman 
Rensselaer Polytechnic Institute 
Troy, NY 
USA 
R. Zdunek 
Wroclaw Univ. Technology 
Wroclaw 
Poland 
S. Zopf 
SVSVistek GmbH 
Munich 
Germany 
The talks
presented at the workshop have been published
as a special issue of the
Electronic
Notes in Discrete Mathematics (Elsevier),
Furthermore,
based
on
some of these
talks we will edit a book entitled Advances
in Discrete Tomography and Its
Applications that will be published by
Birkhäuser Boston (in
2006).