WORKSHOP ON
DISCRETE TOMOGRAPHY
AND ITS APPLICATIONS
June 13-15, 2005
New
York City
Organizers
|
Gabor T. Herman |
Attila Kuba
|
|
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 well-equiped 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 X-Rays 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 Q-convex
Bodies by X-Rays
|
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 X-rays 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 Block-Iterative
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: Multi-Resolution Method
for Binary Tomography
|
|
3:00 - 3:30
|
21. Weber: Prior Learning and
Convex-Concave 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 Discrete-Valued 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 X-Ray
Diffraction Projections Using Gibbs Priors
|
Applications of DT II.
|
11:30 - 12:00
|
29. Krimmel: Discrete Tomography for
Reconstruction from Limited View Angles in Non-Destructive Testing
|
|
12:00 - 12:30
|
30. Rodek: Reconstruction of Pixel-Based
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 |
Cedric-CNAM |
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 |
Garching-Munich |
Germany |
|
A. Kuba |
Univ. Szeged |
Szeged |
Hungary |
|
B. Langfeld |
Techn. Univ. of Munich |
Garching-Munich |
Germany |
|
H. Liao |
Grad. Center, CUNY |
New York, NY |
USA |
|
K. Lord |
Techn. Univ. of Munich |
Garching-Munich |
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 |
Cedric-CNAM |
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 |
Garching-Munich |
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. Vardi-Gonen |
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 |
SVS-Vistek 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).