The FDK algorithm with an expanded definition domain for cone-beam reconstruction preserving oblique line integrals

Journal of X-Ray Science and Technology

Volumn 14, Issue 4, 2006, Pages 217-233

  Li, Liang ^a   Kang, Kejun ^a   Chen, Zhiqiang ^a   Zhang, Li ^a   Xing, Yuxiang ^a   Wang, Ge ^b,c  

^a TSINGHUA UNIVERSITY   (China)

^b UNIVERSITY OF IOWA   (United States)

^c UNIVERSITY OF IOWA   (United States)

Author keywords

Cone beam CT; FBP; FDK; Line integral; Stereogram

Indexed keywords

ALGORITHMS; BACKPROPAGATION; INTEGRATION; MATHEMATICAL TRANSFORMATIONS; OPTICAL FILTERS; X RAY RADIOGRAPHY;

CONE BEAM CT; FILTERED BACKPROJECTION (FBP); LINE INTEGRALS; STEREOGRAMS;

IMAGE RECONSTRUCTION;

EID: 33845546227     PISSN: 08953996     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Radon J Uber die Bestimmung von Funktionene durch ihre Integralwerte langes bestimmter Mannigfaltigkeiten Ber. Verb. Sachs. Akad. Wiss. Leipzig, Math -Nat Kl 69 (1917), 262-277.
2. G.T. Herman and A. Naparstek, Fast image reconstruction based on a radon inversion formula appropriate for rapidly collected data, SIAM J Appl Math 33 (1977), 511-533.
3. F. Natterer The Mathematics of Computerized Tomography, New York: Wiley-Teubner, 1986.
4. A.C. Kak and M. Slaney Principles of Computerized Tomography, Piscataway, NJ: IEEE, 1987.
5. D.L. Parker, Optimal short scan convolution reconstruction for fan-beam CT, Med Phys 9 (1982), 254-257.
6. F. Noo, M. Defrise, R. Clackdoyle and H. Kudo, Image reconstruction from fan-beam projections on less than a short-scan, Phys Med Biol 47 (2002), 2525-2546.
7. H. Kudo, F. Noo, M. Defrise and R. Clackdoyle, New super-short-scan algorithms for fan-beam and cone-beam reconstruction, Conference Record of the 2002 IEEE Nuclear Science Symposium and Medical Imaging Conference, Norfolk, VA, 2003, 902-906.
8. G.H. Chen, A new framework of image reconstruction from fan-beam projections, Med Phys 30 (2003), 1151-1161.
9. A. Katsevich, Theoretically exact FBP-type inversion algorithm for spiral CT, SIAM J Appl Math 62 (2002), 2012-2026.
10. H. Tuy, An inversion formula for cone-beam reconstruction, SIAM J Appl Math 43 (1983), 546-552.
11. Y. Zou and X. Pan, Exact image reconstruction on PI-lines from minimum data in helical cone-beam CT, Phys Med Biol 49 (2004), 941-959.
12. F. Noo, R. Clackdoyle and J.D. Pack, A two-step Hilbert transform method for 2D image reconstruction, Phys Med Biol 49 (2004), 3903-3923.
13. T. Zhuang, S. Leng, B.E. Nett and G.H. Chen, Fan-beam and cone-beam image reconstruction via filtering the backpro-jection image of differentiated projection data, Phys Med Biol 49 (2004), 5489-5503.
14. Y. Zou, X. Pan and E. Sidky, Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan, Phys Med Biol 50 (2005), 13-27.
15. Y. Wei, J. Hsieh and G. Wang, General Formula for Fan-beam Computed Tomography, Phys Rev Let 95 (2005), 258102.
16. L.A. Feldkamp, L.C. Davis and J.W. Kress, Practical cone-beam algorithm, J Opt Soc Am A1 (1984), 612-619.
17. M. Grass, T. Kohler and R. Proksa, 3D cone-beam CT reconstruction for circular trajectories, Phys Med Biol 45 (2000), 329-348.
18. H. Kudo and T. Saito, Helical-scan computed tomography using cone-beam projections, Conference Record of the 1991 IEEE Medical Imaging Conference, Santa Fe, NM (1992) 1958-1962.
19. G. Wang, T.H. Lin, P. Cheng and D.M. Shinozaki, A general cone-beam reconstruction algorithm, IEEE Trans Med Imag MI-12 (1993), 486-496.
20. G. Wang, S.Y. Zhao and P.C. Chen, Exact and approximate cone-beam X-ray micro-tomography, 1995, 233-266.
21. H. Turbell, Cone-beam reconstruction using filtered backprojection, printed in Sweden by UniTryck, Linkoping, February 2001.
22. T. Rodet, F. Noo and M. Defrise, The cone-beam algorithm of Feldkamp, Davis, and Kress preserves oblique line integrals, Med Phys 31 (2004), 1972-1975.
23. H. Hu, An improved cone-beam reconstruction algorithm for the circular orbit, Scanning 18 (1996), 572-581.
24. P. Grangeat Mathematical framework of cone beam 3D reconstruction via derivative of Radon transform. Mathematical Method, in: Tomography, G. Herman, A. Louis and F. Natterer, eds, Lecture Notes in Mathematics, 1991, pp. 66-97.
25. T.H. Lin, G. Wang and P. Cheng, Reconstruction of orthogonal views from cone-beam projections, J Scan Mic 15 (1993), 61-62.
26. L. Li, Z. Chen, Y. Xing, L. Zhang, K. Kang and G. Wang, A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection, Phys Med Biol 51 (2006), 5643-5654.