As the Computed Tomography(CT) requires normally
hundreds of projections to reconstruct the image, patients are exposed
to more X-ray energy, which may cause side effects such as cancer.
Even when the variability of the particles in the object is very less,
Computed Tomography requires many projections for good quality
reconstruction. In this paper, less variability of the particles in an
object has been exploited to obtain good quality reconstruction.
Though the reconstructed image and the original image have same
projections, in general, they need not be the same. In addition
to projections, if a priori information about the image is known,
it is possible to obtain good quality reconstructed image. In this
paper, it has been shown by experimental results why conventional
algorithms fail to reconstruct from a few projections, and an efficient
polynomial time algorithm has been given to reconstruct a bi-level
image from its projections along row and column, and a known sub
image of unknown image with smoothness constraints by reducing the
reconstruction problem to integral max flow problem. This paper also
discusses the necessary and sufficient conditions for uniqueness and
extension of 2D-bi-level image reconstruction to 3D-bi-level image
reconstruction.
[1] G. P. M. Prause and D. G. W. Onnasch, " Binary reconstruction of the
heart chambers from biplane angiographic image sequence", IEEE Trans.
on Medical Imaging, vol. 15, pp. 532-559, 1996.
[2] G. T. Hermann and A. Kuba "Discrete tomography in medical imaging",
Proceedings of the IEEE, vol. 91, pp. 1612-1626, 2003.
[3] A. Kuba, L. Rusko, L. Rodek and Z. Kiss, " Preliminary studies of
discrete tomography in neutron imaging", IEEE Trans. on Nuclear
Science, vol. 52, pp. 375-379, 2005.
[4] G. T. Hermann and A. Kuba, Discrete Tomography Foundations,
Algorithms and Applications Boston: Birkhauser, 1999.
[5] V. Masilamani and K. Krithivasan, "Algorithm for reconstructing 3Dbinary
matrix with periodicity constraints from two projections", Trans.
on Engineering, Computing and Technology, vol. 16, pp. 227-232, 2006.
[6] V. Masilamani and K. Krithivasan, "Bi-Level image reconstruction from
its two orthogonal projections and a sub image", Proc. IEEE - International
Conference on Signal and Image Processing, vol. 1, pp.413-419,
2006.
[7] R. J. Gardner, P. Gritzmann and D. Prangenberg, "On the computational
complexity of reconstructing lattice sets from their X-rays", Discrete
Mathematics, vol. 202, pp. 45-71, 1999.
[8] A. R. Shliferstien and Y. T. Chien, "Switching components and the ambiguity
problem in the reconstruction of pictures from their projections",
Pattern Recognition, vol. 10, pp. 327-340, 1978.
[9] R. W. Irving and M. R. Jerrum, "Three-dimensional statistical data
security problems", SIAM Journal of Computing, vol. 23, pp.170-184,
1994.
[10] C. Kiesielolowski, P. Schwander, F. H. Baumann, M. Seibt, Y. Kim and
A. Ourmazd, "An approach to quantitative high-resolution transmission
electron microscopy of crystalline materials", Ultramicroscopy, vol. 58,
pp. 131-135, 1995.
[11] H. J. Ryser, "Combinatorial properties of matrices of zeroes and ones",
Canad. J. Math., vol. 9, pp. 371-377, 1957.
[12] D. Gale, "A theorem on flows in networks", Pacific. J. Math., vol. 7,
pp. 1073-1082, 1957.
[13] R. J. Gardner and P. Gritzmann, "Discrete tomography: determination of
finite sets by X-rays", Trans. Amer. Math. Soc., vol. 349, pp. 2271-2295,
1997.
[14] S. Matej, A. Vardi, G. T. Hermann and E. Vardi, Discrete tomography
foundations, algorithms, and applications, "chapter Binary tomography
using Gibbs priors", Birkhauser, 1999.
[1] G. P. M. Prause and D. G. W. Onnasch, " Binary reconstruction of the
heart chambers from biplane angiographic image sequence", IEEE Trans.
on Medical Imaging, vol. 15, pp. 532-559, 1996.
[2] G. T. Hermann and A. Kuba "Discrete tomography in medical imaging",
Proceedings of the IEEE, vol. 91, pp. 1612-1626, 2003.
[3] A. Kuba, L. Rusko, L. Rodek and Z. Kiss, " Preliminary studies of
discrete tomography in neutron imaging", IEEE Trans. on Nuclear
Science, vol. 52, pp. 375-379, 2005.
[4] G. T. Hermann and A. Kuba, Discrete Tomography Foundations,
Algorithms and Applications Boston: Birkhauser, 1999.
[5] V. Masilamani and K. Krithivasan, "Algorithm for reconstructing 3Dbinary
matrix with periodicity constraints from two projections", Trans.
on Engineering, Computing and Technology, vol. 16, pp. 227-232, 2006.
[6] V. Masilamani and K. Krithivasan, "Bi-Level image reconstruction from
its two orthogonal projections and a sub image", Proc. IEEE - International
Conference on Signal and Image Processing, vol. 1, pp.413-419,
2006.
[7] R. J. Gardner, P. Gritzmann and D. Prangenberg, "On the computational
complexity of reconstructing lattice sets from their X-rays", Discrete
Mathematics, vol. 202, pp. 45-71, 1999.
[8] A. R. Shliferstien and Y. T. Chien, "Switching components and the ambiguity
problem in the reconstruction of pictures from their projections",
Pattern Recognition, vol. 10, pp. 327-340, 1978.
[9] R. W. Irving and M. R. Jerrum, "Three-dimensional statistical data
security problems", SIAM Journal of Computing, vol. 23, pp.170-184,
1994.
[10] C. Kiesielolowski, P. Schwander, F. H. Baumann, M. Seibt, Y. Kim and
A. Ourmazd, "An approach to quantitative high-resolution transmission
electron microscopy of crystalline materials", Ultramicroscopy, vol. 58,
pp. 131-135, 1995.
[11] H. J. Ryser, "Combinatorial properties of matrices of zeroes and ones",
Canad. J. Math., vol. 9, pp. 371-377, 1957.
[12] D. Gale, "A theorem on flows in networks", Pacific. J. Math., vol. 7,
pp. 1073-1082, 1957.
[13] R. J. Gardner and P. Gritzmann, "Discrete tomography: determination of
finite sets by X-rays", Trans. Amer. Math. Soc., vol. 349, pp. 2271-2295,
1997.
[14] S. Matej, A. Vardi, G. T. Hermann and E. Vardi, Discrete tomography
foundations, algorithms, and applications, "chapter Binary tomography
using Gibbs priors", Birkhauser, 1999.
@article{"International Journal of Information, Control and Computer Sciences:58829", author = "V. Masilamani and C. Vanniarajan and Kamala Krithivasan", title = "On the Reduction of Side Effects in Tomography", abstract = "As the Computed Tomography(CT) requires normally
hundreds of projections to reconstruct the image, patients are exposed
to more X-ray energy, which may cause side effects such as cancer.
Even when the variability of the particles in the object is very less,
Computed Tomography requires many projections for good quality
reconstruction. In this paper, less variability of the particles in an
object has been exploited to obtain good quality reconstruction.
Though the reconstructed image and the original image have same
projections, in general, they need not be the same. In addition
to projections, if a priori information about the image is known,
it is possible to obtain good quality reconstructed image. In this
paper, it has been shown by experimental results why conventional
algorithms fail to reconstruct from a few projections, and an efficient
polynomial time algorithm has been given to reconstruct a bi-level
image from its projections along row and column, and a known sub
image of unknown image with smoothness constraints by reducing the
reconstruction problem to integral max flow problem. This paper also
discusses the necessary and sufficient conditions for uniqueness and
extension of 2D-bi-level image reconstruction to 3D-bi-level image
reconstruction.", keywords = "Discrete Tomography, Image Reconstruction, Projection,
Computed Tomography, Integral Max Flow Problem, Smooth
Binary Image.", volume = "1", number = "9", pages = "2794-6", }