About this Journal Submit a Manuscript Table of Contents
International Journal of Biomedical Imaging
Volume 2012 (2012), Article ID 969432, 12 pages
http://dx.doi.org/10.1155/2012/969432
Research Article

FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT

Department of Electrical Engineering, Indian Institute of Science, Bangalore 560 012, India

Received 5 August 2011; Revised 2 November 2011; Accepted 3 November 2011

Academic Editor: Erik L. Ritman

Copyright © 2012 A. V. Narasimhadhan and Kasi Rajgopal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction, SIAM, Philadelphia, Pa, USA, 2001.
  2. X. Pan, “Optimal noise control in and fast reconstruction of fan-beam computed tomography image,” Medical Physics, vol. 26, no. 5, pp. 689–697, 1999. View at Publisher · View at Google Scholar · View at Scopus
  3. G. L. Zeng, “Nonuniform noise propagation by using the ramp filter in fan-beam computed tomography,” IEEE Transactions on Medical Imaging, vol. 23, no. 6, pp. 690–695, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. X. Pan and L. Yu, “Image reconstruction with shift-variant filtration and its implication for noise and resolution properties in fan-beam computed tomography,” Medical Physics, vol. 30, no. 4, pp. 590–600, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Wang, H. Lu, T. Li, and Z. Liang, “An alternative solution to the nonuniform noise propagation problem in fan-beam FBP image reconstruction,” Medical Physics, vol. 32, no. 11, pp. 3389–3394, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. F. Noo, M. Defrise, R. Clackdoyle, and H. Kudo, “Image reconstruction from fan-beam projections on less than a short scan,” Physics in Medicine and Biology, vol. 47, no. 14, pp. 2525–2546, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. F. Dennerlein, F. Noo, J. Hornegger, and G. Lauritsch, “Fan-beam filtered-backprojection reconstruction without backprojection weight,” Physics in Medicine and Biology, vol. 52, no. 11, article 19, pp. 3227–3240, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. J. You and G. L. Zeng, “Hilbert transform based FBP algorithm for fan-beam CT full and partial scans,” IEEE Transactions on Medical Imaging, vol. 26, no. 2, pp. 190–199, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Kudo, T. Rodet, F. Noo, and M. Defrise, “Exact and approximate algorithms for helical cone-beam CT,” Physics in Medicine and Biology, vol. 49, no. 13, pp. 2913–2931, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. X. Tang, J. Hsieh, A. Hagiwara, R. A. Nilsen, J.-B. Thibault, and E. Drapkin, “A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory,” Physics in Medicine and Biology, vol. 50, no. 16, pp. 3889–3905, 2005. View at Publisher · View at Google Scholar
  11. K. Taguchi, B. S. S. Chiang, and M. D. Silver, “A new weighting scheme for cone-beam helical CT to reduce the image noise,” Physics in Medicine and Biology, vol. 49, no. 11, pp. 2351–2364, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. X. Tang, J. Hsieh, R. A. Nilsen, S. Dutta, D. Samsonov, and A. Hagiwara, “A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT—helical scanning,” Physics in Medicine and Biology, vol. 51, no. 4, pp. 855–874, 2006. View at Publisher · View at Google Scholar
  13. I. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical CB algorithm,” Journal of the Optical Society of America A, vol. 1, no. 6, pp. 612–619, 1984. View at Scopus
  14. G. Wang, T. H. Lin, P. C. Cheng, and D. M. Shinozaki, “General cone-beam reconstruction algorithm,” IEEE Transactions on Medical Imaging, vol. 12, no. 3, pp. 486–496, 1993. View at Publisher · View at Google Scholar · View at Scopus
  15. H. K. Tuy, “An inversion formula for CB reconstruction,” SIAM Journal on Applied Mathematics, vol. 43, no. 3, pp. 546–552, 1983. View at Scopus
  16. B. D. Smith, “Image reconstruction from CB projections: necessary and sufficient conditions and reconstruction methods,” IEEE Transactions on Medical Imaging, vol. 4, no. 1, pp. 14–25, 1985. View at Scopus
  17. J. Hsieh, “A practical cone beam artifact correction algorithm,” in Proceedings of the IEEE Nuclear Science Symposium Conference Record, vol. 2, pp. 71–74, Lyon, France, October 2000. View at Scopus
  18. K. Zeng, Z. Chen, L. Zhang, and G. Wang, “An error-reduction-based algorithm for cone-beam computed tomography,” Medical Physics, vol. 31, no. 12, pp. 3206–3212, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Hu, “An improved CB reconstruction algorithm for the circular orbit,” Scanning, vol. 18, pp. 572–581, 1996.
  20. L. Zhu, J. Starman, and R. Fahrig, “An efficient estimation method for reducing the axial intensity drop in circular cone-beam CT,” International Journal of Biomedical Imaging, vol. 2008, no. 1, Article ID 242841, 11 pages, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. C. Hamaker, K. T. Smith, D. C. Solmon, and S. L. Wagner, “The divergent beam X-Ray transform,” Rocky Mountain Journal of Mathematics, vol. 10, pp. 253–283, 21.
  22. A. V. Narasimhadhan, K. P. Anoop, and K. Rajgopal, “FDK algorithms with no backprojection weight,” in Proceedings of the 10th Fully 3D Meeting and 2nd HPIR Workshop, vol. 10, pp. 158–161, 2009.
  23. A. V. Narasimhadhan and K. Rajgopal, “Helical FDK algorithms with no backprojection weight,” in Proceedings of the IEEE Region 10th Annual International Conference (TENCON '09), 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. P. Grangeat, “Mathematical framework of CB 3D reconstruction via the rst derivative of the Radon transform,” in Mathematical Methods in Tomography, vol. 1497 of Lecture Notes in Mathematics, pp. 66–97, Springer, Berlin, Germany, 1991.
  25. M. Grass, T. Köhler, and R. Proksa, “3D cone-beam CT reconstruction for circular trajectories,” Physics in Medicine and Biology, vol. 45, no. 2, pp. 329–347, 2000. View at Publisher · View at Google Scholar · View at Scopus