A General Cone-Beam Reconstruction Algorithm

IEEE Transactions on Medical Imaging

Volumn 12, Issue 3, 1993, Pages 486-496

  Wang, Ge ^a   Lin, Tein Hsiang ^a   Cheng, Ping Chin ^b   Shinozaki, Douglas M ^b  

^a UNIVERSITY AT BUFFALO   (United States)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; MEDICAL IMAGING; MICROSCOPIC EXAMINATION; X RAY ANALYSIS;

CONE BEAM RECONSTRUCTION ALGORITHM; ROTATION AXIS; SCANNING LOCUS;

IMAGE PROCESSING;

EID: 0027659307     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/42.241876     Document Type: Article

References (47)

1. L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am., vol. 1 (A), pp. 612-619, 1984.
2. P. C. Cheng, S. P. Newberry, H. G. Kim, and M. D. Wittman, “X-ray contact microradiography and shadow projection x-ray microscopy,” Europ. J. Cell Biology, vol. 48, no. 25, pp. 169-172, 1989.
3. P. C. Cheng, S. P. Newberry, H. G. Kim, M. D. Wittman, and I.- S. Hwang, “X-ray contact microradiography and shadow projection microscopy,” in Modern microscopy (P. Duke and A. Michette, eds.), pp. 87-117. New York: Plenum Press, 1990.
4. G. Schmahl and P. C. Cheng, “X-ray microscopy,” in Handbook on Synchrotron Radiation (T.S. E.E. Koch and H.Winick, eds.), vol. 4, pp. 481-536. New York: North-Holland, 1991.
5. P. C. Cheng and G. J. Jan, X-ray Microscopy — Instrumentation and Biological Applications. New York: Springer-Verlag, 1987.
6. P. C. Cheng, D. M. Shinozaki, T. H. Lin, S. P. Newberry, R. Sridhar, W.Tarng, M. T. Chen, and L. H. Chen, “X-ray shadow projection microscopy and microtomography,” in x-ray microscopy — ///, A. Michette, G. R. Monies, and C. J. Buckley, eds. Berlin: Springer-Verlag, 1991.
7. P. C. Cheng, T. H. Lin, D. M. Shinozaki, and S. P. Newberry, “Projection microscopy and microtomography using x-rays,” J. Scanning Microscopy, vol. 13 (I), pp. 10-11, 1991.
8. G. Wang, T. H. Lin, P. C. Cheng, D. M. Shinozaki, and S. P. Newberry, “X-ray projection microscopy and cone-beam microtomography,” in Proc. SPIE, vol. 1398, pp. 180-190, 1991.
9. W. Graeff and K. Engelke, “Microradiography and microtomography,” in Handbook on Synchrotron Radiation, T.S. E.E. Koch and H. Winick, eds., vol. 4, pp. 361-405. New York: North-Holland, 1991.
10. B. D. Smith, “Cone-beam tomography: recent advances and a tutorial review,” Opt. Engineering, vol. 29, pp. 524-534, May 1990.
11. R. M. Lewitt, “Reconstruction algorithms: Transform methods,” Proc. IEEE, vol. 71, pp. 390-408, Mar 1983.
12. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. Piscataway, NJ: IEEE Press, 1987.
13. A. A. Kirillov, “On a problem of I. M. Gel'fand,” Sov. Math. Dokl, vol. 2, pp. 268-269, 1961. English translation.
14. H. K. Tuy, “An inversion formula for cone-beam reconstruction,” SIAM J. Appl. Math., vol. 43, pp. 546-552, 1983.
15. C. Hamaker, D. C. Solmon, and S. L. Wagnor, “The divergent beam x-ray transform,” Rocky Mountain J. Math., vol. 10, pp. 253-259, 1980.
16. O. Nalcioglu and Z. H. Cho, “Reconstruction of 3-D objects from cone-beam projections,” Proc. IEEE, vol. 66, pp. 1584-1585, 1978.
17. R. V. Denton, B. Friedlander, and A. J. Rockmore, “Direct three-dimensional image reconstruction from divergent rays,” IEEE Trans. Nucl. Sci., vol. NS-26, pp. 4695-4703, 1979.
18. K. T. Smith, D. C. Solomon, and S. L. Wagner, “Inversion formulas for the x-ray transform,” Rocky Mount J. Math., vol. 10, pp. 253-283, 1980.
19. K. T. Smith, “Reconstruction formulas in computed tomography,” in Proc. Symposium on Applied Mathematics, vol. 27, pp. 7-23, Am. Math. Soc., 1982.
20. J. Imiya and H. Ogawa, “A direct method of image reconstruction from its line integrals by cone-beam x-rays,” in Proc. Int. Joint Alpine Symp. on Medical Computing, Graphics Image Communication, and Clinical Advances in Neuro CT/NMR, IEEE, pp. 95-101, 1984.
21. F. C. Peyrin, “The generalized backprojection theorem for cone-beam reconstruction,” IEEE Trans. Nucl. Sci, vol. NS-32, pp. 1512-1519, 1985.
22. G. T. Herman, Image Reconstruction from Projections. New York: Academic Press, 1980.
23. R. M. Lewitt and M. R. McKay, “Description of a software package for computing cone-beam x-ray projections of time-varying structures, and for dynamic three-dimensional image reconstruction,” Tech. Rep. MIPG45, Dept. of CS, SUNY/Buffalo, May 1980.
24. R. A. Robb, A. H. Lent, B. K. Gilbert, and A. Chu, “The dynamic spatial reconstructor,” J. Med. Syst., vol. 4, pp. 253-288, 1980.
25. P. Grangeat, “Description of a 3D reconstruction algorithm for diverging x-ray beam,” in Radiology Society of North America Conf. Proc, 1985.
26. P. Grangeat, “3D reconstruction algorithm for diverging x-ray beams,” in CAR ‘85 Conf. Proc, 1985.
27. P. Sire, P. Grangeat, P. Lemasson, P. Melennec, and P. Rizo, “NDT applications of the 3D RADON transform algorithm for cone beam reconstruction,” in Proc. Fall Meeting of the Material Research Soc. (Boston), 1990.
28. G. T. Gullberg, G. L. Zeng, P. E. Christian, B. M. W. Tsui, and H. T. Morgan, “Single photon emission computed tomography of the heart using cone beam geometry and noncircular detector rotation,” in Proc. 11th Int. Conf. on Information Processing in Medical Imaging, pp. 123-138, 1991.
29. G. T. Gullberg and G. L. Zeng, “A cone-beam filtered backprojection reconstruction algorithm for cardiac single photon emission computed tomography,” IEEE Trans. Med. Imag., vol. 11, no. 1, pp. 91-101, 1992.
30. R. J. Jaszczak, K. L. Greer, and R. E. Coleman, “SPECT using a specially designed cone beam collimator,” J. Nuclear Med., vol. 29, pp. 1398-1405, 1988.
31. R. J. Jaszczak, C. E. Floyd, S. H. Manglos, K. L. Greer, and R. E. Coleman, “Cone beam collimation for single photon emission computed tomography: Analysis, simulation, and image reconstruction using filtered backprojection,” Med. Phys., vol. 13, pp. 484-489, 1986.
32. G. Wang, T. H. Lin, P. C. Cheng, and D. M. Shinozaki, “A polygonal cone-beam reconstruction algorithm for x-ray microtomography,” J. Scanning Microscopy, vol. 13 (I), pp. 126-128, 1991.
33. B. D. Smith, “Advances in cone-beam tomography for the analysis of materials,” in Proc. Symp. on Advanced Tomographic Imaging Methods for the Analysis of Materials, Nov. 1990.
34. B. D. Smith, “Cone-beam convolution formula,” Comput. Bio. Med., vol. 13, pp. 81-87, 1983.
35. B. D. Smith, “Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods,” IEEE Trans. Med. Imag., vol. MI-4, pp. 14-28, 1985.
36. B. D. Smith, Computer-aided tomographic imaging from cone-beam data. Ph.D. dissertation, Univ. of Rhode Island, 1987.
37. G. Wang, T.H. Lin, P. C. Cheng, D. M. Shinozaki, and H. Kim, “Scanning cone-beam reconstruction algorithms for x-ray microtomography,” in Proc. SPIE, vol. 1556, pp. 99-113, 1991.
38. G. Wang, T. H. Lin, H. G. Kim, D. M. Shinozaki, and P. C. Cheng, “Cone-beam x-ray microtomography,” chapter 9 in multidimensional Microscopies, P. C. Cheng, T. H. Lin, and W. L. Wu, eds. New York: Springer-Verlag, in press, 1993.
39. T. H. Lin, G. Wang, P. C. Cheng, and D. M. Shinozaki, “A multiple cone-beam projection algorithm for x-ray microtomography,” in X-ray Microscopy—III (A. Michette, G. R. Morrison, and C. J. Buckley, eds.), pp. 296-300 Berlin: Springer-Verlag, 1991.
40. T. H. Lin, G. Wang, P. C. Cheng, and D. M. Shinozaki, “A helical cone-beam reconstruction algorithm for x-ray microtomography,” J. Scanning Microscopy, vol. 13 (I), pp. 11-13, 1991.
41. G. Wang, T. H. Lin, and P. C. Cheng, “A new extended fan-beam reconstruction formula,” in Proc. SPIE, vol. 1660, pp. 262-273, 1992.
42. G. Wang, T. H. Lin, P. C. Cheng, and D. M. Shinozaki, “Point spread function of the general cone-beam x-ray reconstruction formula,” J. Scanning Microscopy, vol. 14, no. 4, pp. 187-193, 1992.
43. X. H. Yan and R. M. Leahy, “Derivation and analysis of a filtered backprojection algorithm for cone beam projection data,” IEEE Trans. Med. Imag., vol. 10, no. 3, pp. 462-472, 1991.
44. G. Wang, T. H. Lin, P. C. Cheng, and D. M. Shinozaki, “Preliminary error analysis on the general cone-beam reconstruction algorithm,” in Proc. SPIE, vol. 1660, pp. 274-285, 1992.
45. F. S. Weinstein, “Formation of images using fan beam scanning and noncircular source motion,” J. Opt. Soc. Amer., vol. 70, pp. 931-935, 1980.
46. B. D. Smith, “Derivation of the extended fan-beam formula,” IEEE Trans. Med. Imag., vol. MI-4, pp. 177-184, 1985.
47. T. H. Lin, G. Wang, and P. C. Cheng, “Error analysis of the general cone-beam reconstruction algorithm for x-ray microtomography,” J. Scanning Microscopy, Suppl. II (Addendum), pp. 20-23, 1992.