CT Reconstruction from a Limited Number of X-Ray Projections
Most CT reconstruction system x-ray computed
tomography (CT) is a well established visualization technique in
medicine and nondestructive testing. However, since CT scanning
requires sampling of radiographic projections from different viewing
angles, common CT systems with mechanically moving parts are too
slow for dynamic imaging, for instance of multiphase flows or live
animals. A large number of X-ray projections are needed to
reconstruct CT images, so the collection and calculation of the
projection data consume too much time and harmful for patient. For
the purpose of solving the problem, in this study, we proposed a
method for tomographic reconstruction of a sample from a limited
number of x-ray projections by using linear interpolation method. In
simulation, we presented reconstruction from an experimental x-ray
CT scan of a Aluminum phantom that follows to two steps: X-ray
projections will be interpolated using linear interpolation method and
using it for CT reconstruction based upon Ordered Subsets
Expectation Maximization (OSEM) method.
[1] K.C. Tam, J. Eberhard, K.W. Mitchell, "Incomplete-data CT image
reconstruction in industrial applications," IEEE Trans. Nucl Sci., vol. 37,
1990, pp. 1490-9.
[2] F. Natterer, The mathematics of computerized tomography. John Wiley &
Sons Ltd, Chichester, 1986.
[3] E.Y. Sidky, C.M. Kao, X. Pan, "Accurate image reconstruction from
few-views and limited-angle data in divergent beam CT," J. X-Ray Sci.
Technol., vol 14, 2006, pp. 119-39.
[4] H.K. Liao, G.T. Herman, "A method for reconstructing label images from
a few projections, as motivated by electron microscopy," IEEE
International Symposium on Biomedical Imaging: Macro to Nano, vol. 1,
2004, pp. 551-4.
[5] G.T. Herman, Image reconstruction from projections: the fundamentals of
computerized tomography. Academic Press, San Francisco 1980.
[6] F. Natterer and F. Wubbeling, Mathematical methods in image
reconstruction. SIAM, Philadelphia (PA) 2001.
[7] A.C. Kak and M. Slaney, Principles of computerized tomographic
imaging. IEEE Press, New York 1988.
[8] P.E. Kinahan, J.A. Fessler and J.S. Karp, "Statistical image reconstruction
in PET with compensation for missing data," IEEE Transactions on
Nuclear Science, vol. 44, 1997, pp. 1552-7.
[9] M.D. Ali and D.Guy, "Maximum entropy image reconstruction in X-ray
adn diffraction tomography," IEEE Transaction on Medical Imaging, vol.
7, 1998, pp. 345-54.
[10] A.J. Reader, "List-mode EM algorithms for limited precision high
resolution PET image reconstruction," International Journal of Imaging
Systems and Technology, vol. 14, 2004, pp. 139-45.
[11] G.T. Herman, A.R. De Pierro and N. Gai, "On method for maximum a
posteriori image reconstruction with a normal prior positron emission
tomography," Journal of Visual Communication and Image
Representation, vol. 3, 1992, pp. 316-24.
[12] B. Deman, J. Nuyts, P. Dupont, G. Marchal and P. Suetens, "An iterative
maximum-likelihood polychromatic algorithm for CT," IEEE
Transactions on Medical Imaging, vol. 20, 2001, pp. 998-1008.
[13] C.L. Byrne, "Iterative image reconstruction algorithms based on
cross-entropy minimization," IEEE Transactions on Image Processing,
vol. 2, 1993, pp. 96-103.
[14] D.J.M. Mohammad K. Islam, H. Alasti and M.B. Sharpe, "Patient dose
from kilovoltage cone beam computed tomography imaging in radiation
therapy," Medical Physics, vol. 73, 2006, pp. 1573-82.
[15] H. H. Nagel, "On the estimation of optical flow: Relations between
different approaches and some new results," Artif. Intell., vol. 33, 1987,
pp. 299-324.
[16] J. L. Barron, D. J. Fleet, and S. S. Beauchemin, "Performace of optical
flow techniques," Int. J. Comput. Vision, vol. 12, 1994, pp. 43-77.
[17] B. K. P. Horm, and B. G. Schunk, "Determining optical flow," Artif.
Intell., vol. 17, 1981, pp. 185-203.
[1] K.C. Tam, J. Eberhard, K.W. Mitchell, "Incomplete-data CT image
reconstruction in industrial applications," IEEE Trans. Nucl Sci., vol. 37,
1990, pp. 1490-9.
[2] F. Natterer, The mathematics of computerized tomography. John Wiley &
Sons Ltd, Chichester, 1986.
[3] E.Y. Sidky, C.M. Kao, X. Pan, "Accurate image reconstruction from
few-views and limited-angle data in divergent beam CT," J. X-Ray Sci.
Technol., vol 14, 2006, pp. 119-39.
[4] H.K. Liao, G.T. Herman, "A method for reconstructing label images from
a few projections, as motivated by electron microscopy," IEEE
International Symposium on Biomedical Imaging: Macro to Nano, vol. 1,
2004, pp. 551-4.
[5] G.T. Herman, Image reconstruction from projections: the fundamentals of
computerized tomography. Academic Press, San Francisco 1980.
[6] F. Natterer and F. Wubbeling, Mathematical methods in image
reconstruction. SIAM, Philadelphia (PA) 2001.
[7] A.C. Kak and M. Slaney, Principles of computerized tomographic
imaging. IEEE Press, New York 1988.
[8] P.E. Kinahan, J.A. Fessler and J.S. Karp, "Statistical image reconstruction
in PET with compensation for missing data," IEEE Transactions on
Nuclear Science, vol. 44, 1997, pp. 1552-7.
[9] M.D. Ali and D.Guy, "Maximum entropy image reconstruction in X-ray
adn diffraction tomography," IEEE Transaction on Medical Imaging, vol.
7, 1998, pp. 345-54.
[10] A.J. Reader, "List-mode EM algorithms for limited precision high
resolution PET image reconstruction," International Journal of Imaging
Systems and Technology, vol. 14, 2004, pp. 139-45.
[11] G.T. Herman, A.R. De Pierro and N. Gai, "On method for maximum a
posteriori image reconstruction with a normal prior positron emission
tomography," Journal of Visual Communication and Image
Representation, vol. 3, 1992, pp. 316-24.
[12] B. Deman, J. Nuyts, P. Dupont, G. Marchal and P. Suetens, "An iterative
maximum-likelihood polychromatic algorithm for CT," IEEE
Transactions on Medical Imaging, vol. 20, 2001, pp. 998-1008.
[13] C.L. Byrne, "Iterative image reconstruction algorithms based on
cross-entropy minimization," IEEE Transactions on Image Processing,
vol. 2, 1993, pp. 96-103.
[14] D.J.M. Mohammad K. Islam, H. Alasti and M.B. Sharpe, "Patient dose
from kilovoltage cone beam computed tomography imaging in radiation
therapy," Medical Physics, vol. 73, 2006, pp. 1573-82.
[15] H. H. Nagel, "On the estimation of optical flow: Relations between
different approaches and some new results," Artif. Intell., vol. 33, 1987,
pp. 299-324.
[16] J. L. Barron, D. J. Fleet, and S. S. Beauchemin, "Performace of optical
flow techniques," Int. J. Comput. Vision, vol. 12, 1994, pp. 43-77.
[17] B. K. P. Horm, and B. G. Schunk, "Determining optical flow," Artif.
Intell., vol. 17, 1981, pp. 185-203.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:53900", author = "Tao Quang Bang and Insu Jeon", title = "CT Reconstruction from a Limited Number of X-Ray Projections", abstract = "Most CT reconstruction system x-ray computed
tomography (CT) is a well established visualization technique in
medicine and nondestructive testing. However, since CT scanning
requires sampling of radiographic projections from different viewing
angles, common CT systems with mechanically moving parts are too
slow for dynamic imaging, for instance of multiphase flows or live
animals. A large number of X-ray projections are needed to
reconstruct CT images, so the collection and calculation of the
projection data consume too much time and harmful for patient. For
the purpose of solving the problem, in this study, we proposed a
method for tomographic reconstruction of a sample from a limited
number of x-ray projections by using linear interpolation method. In
simulation, we presented reconstruction from an experimental x-ray
CT scan of a Aluminum phantom that follows to two steps: X-ray
projections will be interpolated using linear interpolation method and
using it for CT reconstruction based upon Ordered Subsets
Expectation Maximization (OSEM) method.", keywords = "CT reconstruction, X-ray projections, Interpolation
technique, OSEM", volume = "5", number = "10", pages = "1965-3", }