A general scheme for constructing inversion algorithms for cone beam CT

International Journal of Mathematics and Mathematical Sciences

Volumn 2003, Issue 21, 2003, Pages 1305-1321

  Katsevich, Alexander ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042903710     PISSN: 01611712     EISSN: None     Source Type: Journal    
DOI: 10.1155/S0161171203209315     Document Type: Article

References (20)

1. T. Aubin, A Course in Differential Geometry, Graduate Studies in Mathematics, vol. 27, American Mathematical Society, Rhode Island, 2001. MathSciNet. Zentralblatt für Mathematik.
2. P. E. Danielsson et al., Towards exact reconstruction for helical cone-beam scanning of long objects. A new detector arrangement and a new completeness condition, Proc. 1997 Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine (Pittsburgh) (D. W. Townsend and P. E. Kinahan, eds.), 1997, pp. 141-144.
3. M. Defrise and R. Clack, A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection, IEEE Trans. on Medical Imaging 13 (1994), 186-195. CrossRef.
4. M. Defrise, F. Noo, and H. Kudo, A solution to the long-object problem in helical cone-beam tomography, Phys. Med. Biol. 45 (2000), 623-643. CrossRef.
5. D. V. Finch, Cone beam reconstruction with sources on a curve, SIAM J. Appl. Math. 45 (1985), no. 4, 665-673. MathSciNet. Zentralblatt für Mathematik.
6. I. M. Gelfand and A. B. Goncharov, Recovery of a compactly supported function starting from its integrals over lines intersecting a given set of points in space, Soviet Math. Dokl. 34 (1987), 373-376. Zentralblatt für Mathematik.
7. P. Grangeat, Mathematical framework of cone beam $3$D reconstruction via the first derivative of the Radon transform, Mathematical Methods in Tomography (Oberwolfach, 1990) (G. T. Herman, A. K. Louis, and F. Natterer, eds.), Lecture Notes in Math., vol. 1497, Springer, Berlin, 1991, pp. 66-97. MathSciNet. Zentralblatt für Mathematik.
8. A. Greenleaf and G. Uhlmann, Nonlocal inversion formulas for the X-ray transform, Duke Math. J. 58 (1989), no. 1, 205-240. MathSciNet. Zentralblatt für Mathematik.
9. A. Katsevich, On quasi-local inversion of spiral CT data, Math. Methods Appl. Sci. 23 (2000), no. 3, 271-297. CrossRef. MathSciNet. Zentralblatt für Mathematik.
10. A. Katsevich, Improved exact FBP algorithm for spiral CT, Preprint, 2001.
11. A. Katsevich, An inversion algorithm for Spiral CT, Proceedings of the 2001 International Conference on Sampling Theory and Applications (A. I. Zayed, ed.), University of Central Florida, Florida, 2001, pp. 261-265.
12. A. Katsevich, Theoretically exact filtered backprojection-type inversion algorithm for spiral CT, SIAM J. Appl. Math. 62 (2002), no. 6, 2012-2026. MathSciNet.
13. H. Kudo and T. Saito, Derivation and implementation of a cone-beam reconstruction algorithm for non-planar orbits, IEEE Trans. on Medical Imaging 13 (1994), 196-211. CrossRef.
14. H. Kudo and T. Saito, Fast and stable cone-beam filtered backprojection method for non-planar orbits, Phys. Med. Biol. 43 (1998), 747-760. CrossRef.
15. F. Natterer, Recent developments in X-ray tomography, Tomography, Impedance Imaging, and Integral Geometry (South Hadley, Mass, 1993), Lectures in Appl. Math., vol. 30, American Mathematical Society, Rhode Island, 1994, pp. 177-198. MathSciNet. Zentralblatt für Mathematik.
16. E. T. Quinto, Singularities of the X-ray transform and limited data tomography in $\mathbf{R}̂2$ and $\mathbf{R) ̂3$, SIAM J. Math. Anal. 24 (1993), no. 5, 1215-1225. MathSciNet. Zentralblatt für Mathematik.
17. A. G. Ramm and A. I. Zaslavsky, X-ray transform, the Legendre transform, and envelopes, J. Math. Anal. Appl. 183 (1994), no. 3, 528-546. CrossRef. MathSciNet. Zentralblatt für Mathematik.
18. B. Smith, Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods, IEEE Trans. on Medical Imaging 4 (1985), 14-25.
19. H. Turbell and P.-E. Danielsson, Helical cone beam tomography, Int. J. of Imaging Syst. and Technology 11 (2000), 91-100. CrossRef.
20. H. K. Tuy, An inversion formula for cone-beam reconstruction, SIAM J. Appl. Math. 43 (1983), no. 3, 546-552. MathSciNet.