Feasible cone beam scanning methods for exact reconstruction in three-dimensional tomography

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 7, Issue 12, 1990, Pages 2169-2183

  Kudo, Hiroyuki ^a   Saito, Tsuneo ^b  

^a TOHOKU UNIVERSITY   (Japan)

^b UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; CAT; FOURIER ANALYSIS; IMAGE PROCESSING; MATHEMATICS; METHODOLOGY; TOMOGRAPHY;

ALGORITHMS; ANIMAL; CATS; FOURIER ANALYSIS; IMAGE PROCESSING, COMPUTER-ASSISTED; MATHEMATICS; TOMOGRAPHY, X-RAY COMPUTED;

EID: 0025654010     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.7.002169     Document Type: Article

References (29)

1. R. A. Robb, A. H. Lent, B. K. Gilbert, and A. Chu, “The dynamic spatial reconstructor,” J. Med. Syst. 4, 253-288 (1980).
2. 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. 13, 484-489 (1986).
3. L. A. Shepp and B. F. Logan, “The Fourier reconstruction of a head section,” IEEE Trans. Nucl. Sei. NS-21, 21-43 (1974).
4. R. V. Denton, B. Friedlander, and A. J. Rockmore, “Direct three-dimensional image reconstruction from divergent rays,” TEEE Trans. Nucl. Sei. NS-26,4695-4703 (1979).
5. O. Nalcioglu and Z. H. Cho, “Reconstruction of 3-D objects from cone beam projections,” Proc. IEEE 66,1584-1585 (1978).
6. F. C. Peyrin, “The generalized back-projection theorem for cone-beam reconstruction,” IEEE Trans. Nucl. Sei. NS-32, 1512-1519 (1985).
7. S. Z. Lee, J. B. Ra, S. K. Hilal, and Z. H. Cho, “True threedimensional cone-beam reconstruction (TTCR) algorithm,” IEEE Trans. Med. Imaging 8, 304-312 (1989).
8. G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980), Chap. 14.
9. L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone- beam algorithm,” J. Opt. Soc. Am. A 1,612-619 (1984).
10. S. Webb, J. Sutcliffe, L. Burkinshaw, and A. Horsman, “Tomographic reconstruction from experimentally obtained cone- beam projections,” IEEE Trans. Med. Imaging MI-6, 67-73 (1987).
11. A. Lent and H. Tuy, “An iterative method for the extrapolation of band-limited functions,” J. Math. Anal. Appl. 83, 554-565 (1981).
12. B. D. Smith, “Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods,” IEEE Trans. Med. Imaging MI-4,14-25 (1985).
13. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, New York, 1988), Chap. 3.
14. A. A. Kirillov, “On a problem of I. M. Gel’fand,” Sov. Math. Dokl. 2, 268-269 (1961).
15. H. K. Tuy, “An inversion formula for cone-beam reconstruction,” SIAM J. Appl. Math. 43, 546-552 (1983).
16. B. D. Smith, “Cone beam convolution formula,” Comput. Biol. Med. 13,81-87 (1983).
17. H. Kudo and T. Saito, “Feasible cone beam scanning methods for exact 3-D tomographic image reconstruction,” in Digest of Topical Meeting on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), pp. 174-177.
18. B. K. P. Horn, “Density reconstruction using arbitrary raysampling scheme,” Proc. IEEE 66,551-562 (1978).
19. M. Chiu, H. H. Barrett, and R. G. Simpson, “Three-dimensional reconstruction from planar projections,” J. Opt. Soc. Am. 70, 755-762 (1980).
20. L. A. Shepp, “Computerized tomography and nuclear magnetic resonance,” J. Comput. Assist. Tomogr. 4,94-107 (1980).
21. H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Chap. 9.
22. H. Kudo and T. Saito, “3-D tomographic image reconstruction from incomplete cone beam projections,” in Digest of Topical Meeting on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), pp. 170-173.
23. H. Hu, R. A. Kruger, and G. T. Gullberg, “Quantitative cone- beam reconstruction,” in Medical Imaging III: Image Processing, R. H. Schneider, S. J. Dwyer III, and R. G. Jost, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1092,492-501 (1989).
24. G. N. Ramachandran and A. V. Lakshminarayanan, “Three dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sei. USA 68, 2236-2240 (1971).
25. S. W. Lee and Z. H. Cho, “Limited angular view planar-integral projection reconstruction in NMR imaging,” IEEE Trans. Nucl. Sei. NS-31,974-982 (1984).
26. S. X. Pan and A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31,1262-1275 (1983).
27. L. A. Shepp and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113-122 (1982).
28. R. M. Lewitt, “Processing of incomplete measurement data in computed tomography,” Med. Phys. 6,412-417 (1979).
29. F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986), p. 56.