Some Mathematical Concepts for Tomographic Reconstruction

Advanced Tomographic Methods in Materials Research and Engineering

Volumn 9780199213245, Issue , 2008, Pages

  Kuba, Attila ^a   Herman, Gabor T ^b  

^a UNIVERSITY OF SZEGED   (Hungary)

^b CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Algebraic reconstruction; Beam hardening; Discrete tomography; Filtered backprojection; Reconstruction methods

Indexed keywords

ALGEBRA;

ALGEBRAIC RECONSTRUCTION; BEAM HARDENING; DISCRETE TOMOGRAPHY; FILTERED BACK-PROJECTION; RECONSTRUCTION METHOD;

TOMOGRAPHY;

EID: 84922760995     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780199213245.003.0002     Document Type: Chapter

References (35)

1. Alpers, A., Poulsen, H.F., Knudsen, E., and Herman, G.T. (2006). A discrete tomography algorithm for improving the quality of three-dimensional X-ray diffraction grain maps. Journal of Applied Crystallography, 39, 582.
2. Andersen, A.H. and Kak, A.C. (1984). Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm. Ultrasonic Imaging, 6, 81.
3. Bocage, A.E.M. (1922). Procédé et dispositif de radiographie sur plaque en mouvement. Brevet francais, 534, 464.
4. Carazo, J-M., Herman, G.T., Sorzano, C.O.S., and Marabini, R. (2006). Algorithms for three-dimensional reconstruction from the imperfect projection data provided by electron microscopy. In Electron tomography: methods for three-dimensional visualization of structures in the cell (2nd edn) (ed. J. Frank), pp. 217. Springer, New York.
5. Censor, Y. and Zenios, S.A. (1997). Parallel optimization: theory and algorithms. Oxford University Press, New York.
6. Chan, M.T., Herman, G.T., and Levitan, E. (1999). Probabilistic modeling of discrete images. In Discrete tomography. Foundations, algorithms, and applications (ed. G. Herman and A. Kuba), pp. 213. Birkhäuser, Boston.
7. CUNY Institute for Software Design and Development (2007). Snark05 [programming system].. [Online; accessed 26 April 2007].
8. Edholm, P.R. and Herman, G.T. (1987). Linograms in image reconstruction from projections. IEEE Transactions on Medical Imaging, 6, 301.
9. Edholm, P.R., Herman, G.T., and Roberts, D.A. (1988). Image reconstruction from linograms - Implementation and evaluation. IEEE Transactions on Medical Imaging, 7, 239.
10. Eggermont, P.P.B., Herman, G.T., and Lent, A. (1981). Iterative algorithms for large partitioned linear systems with applications to image reconstruction. Linear Algebra and its Applications, 37, 40.
11. Gilbert, P. (1972). Iterative methods for three-dimensional reconstruction of an object from projections. Journal of Theoretical Biology, 36, 105.
12. Gordon, R., Bender, R., and Herman, G.T. (1970). Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology, 29, 471.
13. Herman, G.T. (1979). Correction for beam hardening in computed tomography. Physics in Medicine and Biology, 24, 81.
14. Herman, G.T. (1980). Image reconstruction from projections. The fundamentals of computerized tomography. Academic Press, New York.
15. Herman, G.T. and Kuba, A. (1999). Discrete tomography. Foundations, algorithms, and applications. Birkhäuser, Boston.
16. Herman, G.T. and Kuba, A. (2006). Optimization in the medical applications of discrete tomography. Society of Industrial and Applied Mathematics Activity Group -SIAG/Optimization Views-and-News, 17, 2.
17. Herman, G.T. and Kuba, A. (2007). Advances in discrete tomography and its applications. Birkhäuser, Boston.
18. Herman, G.T. and Meyer, L.M. (1993). Algebraic reconstruction techniques can be made computationally efficient. IEEE Transactions on Medical Imaging, 12, 600.
19. Jennings, R.J. (1988). A method for comparing beam hardening filter materials for diagnostic radiology. Medical Physics, 15, 588.
20. Joseph, P.M. and Spittal, A. (1978). A method for correcting bone induced artifacts in computed tomography scanners. Medical Physics, 2, 100.
21. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220, 671.
22. Kuba, A., Ruskó, L., L. Rodek, and Kiss, Z. (2005). Preliminary studies of discrete tomography in neutron imaging. IEEE Transactions on Nuclear Science, 52, 380.
23. Lewitt, R.M. (1990). Multidimensional digital image representation using generalized Kaiser-Bessel window functions. Journal of the Optical Society of America A, 7, 1834.
24. Matej, S., Herman, G.T., Narayan, T.K., Furuie, S.S, Lewitt, R.M., and Kinahan, P.E. (1994). Evaluation of task-oriented performance of several fully 3D PET reconstruction algorithms. Physics in Medicine and Biology, 39, 355.
25. Matej, S. and Lewitt, R.M. (1996). Practical considerations for 3-D image reconstruction using spherically symmetric volume elements. IEEE Transactions on Medical Imaging, 15, 68.
26. Mohammad-Djafari, A. and Sauer, K. (1998). Shape reconstruction in X-ray tomography from a small number of projections using deformable models. In Maximum entropy and Bayesian methods (ed. J. Rychert and G. Erickson), pp. 1. Kluwer Academic, Norwell.
27. Mueller, K. and Yagel, R. (1996). Rapid 3D cone-beam reconstruction with SART using texture mapping hardware. IEEE Transactions on Medical Imaging, 19, 1227.
28. Natterer, F. (1986). The mathematics of computerized tomography. Teubner, Stuttgart.
29. Radermacher, M. (1988). Three-dimensional reconstruction of single particles from random and nonrandom tilt series. Journal of Electron Microscopy Technique, 9, 359.
30. Radon, J. (1917). Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte über die Verhandlungen der Königlichen Sächsischen Akademie der Wissenschaften, 69, 262.
31. Ramachandran, G.N. and Lakshminarayanan, A.V. (1971). Three-dimensional reconstruction from radiographs and electron micrographs: Application of convolutions instead of Fourier transforms. Proceedings of the National Academy of Sciences of the USA, 68, 2236.
32. Shepp, L.A. and Logan, B.F. (1974). The Fourier reconstruction of a head section. IEEE Transactions on Nuclear Science, 21, 21.
33. Shepp, L.A. and Vardi, Y. (1982). Maximum likelihood reconstruction in emission tomography. IEEE Transactions on Medical Imaging, 1, 113.
34. Sorzano, C.O.S., Marabini, R., Boisset, N., Rietzel, E., Schröder, R., Herman, G.T., and Carazo, J.M. (2001). The effect of overabundant projection directions on 3D reconstruction algorithms. Journal of Structural Biology, 133, 108.
35. Vardi, E., Herman, G.T., and Kong, T.Y. (2001). Speeding up stochastic reconstructions of binary images from limited projection directions. Linear Algebra and its Applications, 339, 75.