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Article information
2004 , Volume 9, ¹ 5, p.14-32
Yasar O., Diner C., Dogan A., Weber G.W., Ozbudak F., Tiefenbach A.
On the applied mathematics of discrete tomography
Applied mathematics is very much concerned with inverse problems of reconstruction having applications in geology, geodesics, medicine, economy and technology. In the last decades tomographical problems appeared as an important class of inverse problems, and insights into their solutions gave rise to the development of computerized tomography. Conventional computerized tomography deals with the spatial distribution of a continuous variable, whose resolution is limited with the number of projections. Discrete Tomography arised as a solution of this limitation of discretizing the continuous variable. In Discrete Tomography we try to reconstruct a discrete set from its projections. In this paper, we survey the foundations of the subject and we give our contributions. The connection of Discrete Tomography to other fields of mathematics and its practical applications will be given. The problems of consistency, uniqueness and reconstruction will be defined and their complexities examined. Additivity and uniqueness, being the most important properties of the problem will be demonstrated. Recent contributions and impulses, open problems and future research projects will be mentioned.
[full text] Classificator Msc2000:- *39A12 Discrete version of topics in analysis
- 92C55 Biomedical imaging and signal processing
- 44A12 Radon transform
Keywords: lattice, feasibility problem, optimization problem, discrete Radon base
Author(s):
Yasar O
Office: Institute of Applied Mathematics, Mathematics Department
Address: Turkey, Ankara
E-mail: oznur@tore.math.metu.edu.tr
Diner C.
Office: Institute of Applied Mathematics, Mathematics Department
Address: Turkey, Ankara
E-mail: oznur@tore.math.metu.edu.tr
Dogan A.
Office: Institute of Applied Mathematics, Mathematics Department
Address: Turkey, Ankara
E-mail: oznur@tore.math.metu.edu.tr
Weber GerhardW.
Office: Institute of Applied Mathematics, METU
Address: 64289, Turkey, Ankara
E-mail: gweber@metu.edu.tr
Ozbudak F.
Office: Institute of Applied Mathematics, METU, Mathematics Department
Address: Turkey, Ankara, Ankara
Tiefenbach A.
Office: Institute of Applied Mathematics, METU, Mathematics Department
Address: Turkey, Ankara, Ankara
Bibliography link:
Yasar O., Diner C., Dogan A., Weber G.W., Ozbudak F., Tiefenbach A. On the applied mathematics of discrete tomography // Computational technologies. 2004. V. 9. ¹ 5. P. 14-32
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