Efficient projection and backprojection scheme for spherically symmetric basis functions in divergent beam geometry

Medical Physics

Volumn 33, Issue 12, 2006, Pages 4653-4663

  Ziegler, Andy ^a   Köhler, Thomas ^a   Nielsen, Tim ^a   Proksa, Roland ^a  

^a PHILIPS RESEARCH LABORATORIES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTERIZED TOMOGRAPHY; FUNCTIONS; GEOMETRY; IMAGE QUALITY; ITERATIVE METHODS; LOW PASS FILTERS;

BACK-PROJECTION; CONE BEAM RECONSTRUCTION; DIVERGENT BEAMS; HIGH-RESOLUTION RECONSTRUCTION; ITERATIVE RECONSTRUCTION ALGORITHMS; LOW-PASS FILTERING; SPATIAL POSITIONS; SPHERICALLY SYMMETRIC BASIS FUNCTIONS;

IMAGE RECONSTRUCTION;

CESIUM 137;

ARTICLE; CONE BEAM TRANSMISSION TOMOGRAPHY; DIVERGENT BEAM GEOMETRY; FILTRATION; GEOMETRY; IMAGE QUALITY; IMAGE RECONSTRUCTION; PRIORITY JOURNAL;

EID: 33845323407     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.2388570     Document Type: Article

References (37)

1. G. N. Watson, Theory of Bessel Functions (Cambridge University Press, Cambridge, 1944).
2. S. Matej and R. Lewitt, " Practical considerations for 3D image reconstruction using spherically symmetric volume elements., " IEEE Trans. Med. Imaging 15 (1), 68-78 (l996).
3. T. Obi, S. Matej, R. M. Lewitt, and G. T. Herman, " 2.5-D simultaneous multislice reconstruction by series expansion methods from Fourier-rebinned PET data., " IEEE Trans. Med. Imaging 19 (5), 474-484 (2000).
4. M. E. Daube-Witherspoon, S. Matej, J. S. Karp, and R. M. Lewitt, " Application of the row action maximum likelihood algorithm with spherical basis functions to clinical PET imaging., " IEEE Trans. Nucl. Sci. 48 (1), 24-30 (2001).
5. Th. Köhler, R. Proksa, and T. Nielsen, " SNR-weighted ART applied to transmission tomography., " in Nuclear Science Symposium Conference Record (IEEE, New York, 2003), pp. 2739-2742.
6. B. M. Carvalho and G. T. Herman, " Helical CT reconstruction from wide cone-beam angle data using ART., " SIBGRAPI 2003, XVI Brazilian Symposium on Computer Graphics and Image Processing, 2003, pp. 363-370.
7. K. Mueller, R. Yagel, and J. J. Wheller, " Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods., " IEEE Trans. Med. Imaging 18 (6), 519-537 (1999).
8. A. Yendiki and J. A. Fessler, " A comparison of rotation- and blob-based system model for 3D SPECT with depth-dependent detector response., " Phys. Med. Biol. 49, 2157-2168 (2004).
9. S. Staelens, Y. D 'Asseler, S. Vandenberghe, M. Koole, I. Lemahieu, and R. Van de Walle, " A three-dimensional theoretical model incorporating spatial detector uncertainty in continuous detector PET., " Phys. Med. Biol. 49, 2337-2350 (2004).
10. L. M. Popescu and R. M. Lewitt, " Ray tracing through a grid of blobs., " in Nuclear Science Symposium Conference Record (IEEE, New York, 2004), pp. 3983-3986.
11. T. Nielsen, A. Ziegler, Th. Köhler, and R. Proksa, " Imaging method with back projection., " Patents EP 04102956.2 and WO 2006000997, 2004.
12. A. Ziegler, Th. Köhler, T. Nielsen, and R. Proksa, " Iterative cone-beam CT image reconstruction with spherically symmetric basis functions., " Proceedings of the 3D'2005 Conference, Salt Lake City, UT 2005, pp. 80-83.
13. R. M. Lewitt, " Alternatives to voxels for image representation in iterative reconstruction algorithms., " Phys. Med. Biol. 37 (3), 705-716 (1992).
14. R. M. Lewitt, " Multidimensional digital image representations using generalized Kaiser-Bessel window functions., " J. Opt. Soc. Am. A 7 (10), 1834-1846 (1990).
15. Image Reconstruction from Projections-The Fundamentals of Computerized Tomography, Computer Science and Applied Mathematics, edited by, G. T. Herman, (Academic, New York, 1980).
16. R. L. Siddon, " Fast calculation of the exact radiological path length for a three-dimensional CT array., " Med. Phys. 12, 252-255 (1985).
17. W. Zhuang, S. Gopal, and T. Hebert, " Numerical evaluation of methods for computing tomographic projections., " IEEE Trans. Nucl. Sci. 41 (4), 1660-1665 (1994).
18. F. Beekman and C. Kamphuis, " Ordered subset reconstruction for x-ray CT., " Med. Phys. 46, 1835-1844 (2001).
19. B. De Man and S. Basu, " Distance-driven projection and backprojection in three dimensions., " Phys. Med. Biol. 49, 2463-2475 (2004).
20. K. Mueller, R. Yagel, and J. J. Wheller, " Fast implementations of algebraic methods for three-dimensional reconstruction from cone-beam data., " IEEE Trans. Med. Imaging 18 (6), 538-548 (1999).
21. A. Andersen and A. Kak, " Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm., " Ultrason. Imaging 6, 81-94 (1984).
22. R. Gordon, R. Bender, and G. T. Herman, " Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography., " J. Theor. Biol. 29, 471-481 (1970).
23. J. A. Fessler, " Statistical image reconstruction methods for transmission tomography., " in Handbook of Medical Imaging, edited by, J. M. Fritzpatrick, and, M. Sonka, (SPIE, Bellingham, WA, 2000), Vol. 2, Chap., pp. 1-70.
24. L. A. Feldkamp, L. C. Davis, and J. W. Kress, " Practical cone-beam algorithm., " J. Opt. Soc. Am. A 6, 612-619 (1984).
25. H. K. Tuy, " 3D image reconstruction for helical partial cone-beam scanners using wedge beam transform., " US Patent No. 6,104,775, 2000.
26. K. M. Brown, D. J. Heuscher, and P. Kling, " Conebeam computed tomography imaging., " US Patent No. 6,775,346, 2002.
27. A. Katsevich, " Theoretically exact fbp-type inversion algorithm for spiral CT., " in Proceedings of the 3D'2001 Conference, Asilomar, USA, 2001, pp. 3-6.
28. H. Guan and R. Gordon, " A projection access order for speedy convergence of ART (algebraic reconstruction technique): A multilevel scheme for computed tomography., " Phys. Med. Biol. 39, 2005-2022 (1994).
29. H. Guan and R. Gordon, " Computed tomography using algebraic reconstruction techniques (ARTs) with different projection access schemes: A comparison study under practical situations., " Phys. Med. Biol. 41, 1727-1743 (1996).
30. Th. Köhler, " A projection access scheme for iterative reconstruction based on the golden section., " Proceedings of the IEEE Medical Imaging Conference, Rome, Italy, 2004.
31. T. M. Peters and R. M. Lewitt, " Computed tomography with fan-beam geometry., " J. Comput. Assist. Tomogr. 1 (4), 429-436 (1977).
32. http://www.imp.uni-erlangen.de/forbild
33. D. L. Snyder, M. I. Miller, L. J. Thomas, and D. G. Politte, " Noise and edge artifacts in maximum-likelihood reconstruction for emission tomography., " IEEE Trans. Med. Imaging 6 (3), 228-238 (1987).
34. J. Nuyts, B. De Man, P. Dupon, M. Defrise, P. Suetens, and L. Mortelmans, " Iterative reconstruction for helical CT: A simulation study., " Phys. Med. Biol. 43, 729-737 (l998).
35. W. Zbijewski and F. J. Beekman, " Characterization and suppression of edge and aliasing artefacts in iterative x-ray CT reconstruction., " Phys. Med. Biol. 49 (1) 145-157 (2004).
36. W. Zbijewski and F. J. Beekman, " Comparison of methods for suppressing edge and aliasing artifacts in iterative x-ray CT reconstruction., " Phys. Med. Biol. 51 (1), 1877-1889 (2006).
37. A. Ziegler, T. Nielsen, and M. Grass, " Iterative reconstruction of a region of interest for transmission tomography., " Proc. SPIE, 6142, 614223 (2006).