Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction

IEEE Transactions on Medical Imaging

Volumn 25, Issue 5, 2006, Pages 582-589

  Zhang O'Connor, Yingying ^a,b   Fessler, Jeffrey A ^a,b  

^a IEEE   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Fan beam tomography; Iterative tomographic image reconstruction; Min max interpolation; Nonuniform FFT

Indexed keywords

FAN-BEAM TOMOGRAPHY; ITERATIVE TOMOGRAPHIC IMAGE RECONSTRUCTION; MIN-MAX INTERPOLATION; NONUNIFORM FFT;

COMPUTER SIMULATION; COMPUTERIZED TOMOGRAPHY; DATA ACQUISITION; FAST FOURIER TRANSFORMS; INTERPOLATION; ITERATIVE METHODS;

IMAGE RECONSTRUCTION;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER ASSISTED TOMOGRAPHY; EVALUATION; FOURIER ANALYSIS; HUMAN; IMAGE QUALITY; INFORMATION RETRIEVAL; INSTRUMENTATION; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; THREE DIMENSIONAL IMAGING;

ALGORITHMS; FOURIER ANALYSIS; HUMANS; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; PHANTOMS, IMAGING; RADIOGRAPHIC IMAGE ENHANCEMENT; RADIOGRAPHIC IMAGE INTERPRETATION, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; TOMOGRAPHY, X-RAY COMPUTED;

EID: 33646397021     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2006.872139     Document Type: Article

References (30)

1. J. A. Fessler and B, P. Sutton, "A min-max approach to the multidimensional nonuniform FFT: application to tomographic image reconstruction," in Proc. IEEE Int. Conf. Image Processing, 2001, vol. 1, pp. 706-709.
2. J. A. Fessler. Iterative Tomographic Image Reconstruction Using Nonuniform Fast Fourier Transforms Tech. Rep., Comm. and Signal Process. Lab., Dept. EECS, Univ. Michigan, Ann Arbor, MI, 48 109-2122, Dec. 2001 [Online], Available:http://www.eecs.umich.edu/~fessler, Technical report available from
3. S. Matej. J. A. Fessler, and I. G. Kazantsev, Fourier-Based Forward and Back-Projectors for Iterative Image Reconstruction Univ. Pennsylvania, Philadelphia, Tech. Rep. MIPG303, May 2003.
4. _, "Iterative tomographic image reconstruction using Fourier-based forward and back-projectors," IEEE Trans. Med. Imag., vol. 23, no. 4, pp. 401-412, Apr. 2004.
5. J. A. Fessler and B. P. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 560-574, Feb. 2003.
6. Y. Zhang and J. A. Fessler, "Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction," in Proc. IEEE Int. Symp. Biomedical Imaging, 2004, pp. 364-367.
7. G.-H. Chen, S. Leng, and C. A. Mistretta, "A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections," Med. Phys., vol. 32, no. 3, pp. 654-665, Mar. 2005.
8. S. De Francesco and A. M. Ferreira da Silva, "Efficient NUFFT-based direct Fourier algorithm for fan beam CT reconstruction," Proc. SPIE, vol. 5370, Medical Imaging 2004: Image Processing, pp. 666-677, 2004.
9. K. Fourmont, "Non-equispaeed fast Fourier transforms with applications to tomography," J. Fourier Anal. and Appl., vol. 9, no. 5, pp. 431-450, Sep. 2003.
10. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. Piscataway, NJ: IEEE Press, 1988.
11. G. Besson, "CT fan-beam parametrizations leading to shift-invariant filtering," Inverse Prob., vol. 12, no. 6, pp. 815-833, Dec. 1996.
12. H. Peng and H. Stark, "Direct Fourier reconstruction in fan-beam tomography," IEEE Trans. Med. Imag., vol. 6, no. 3, pp. 209-219, Sep. 1987.
13. J. D. O'Sullivan, "A fast sine function gridding algorithm for Fourier inversion in computer tomography," IEEE Trans. Med. Imag., vol. 4, no. 4, pp. 200-207, Dec. 1985.
14. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski, "Selection of a convolution function for Fourier inversion using gridding," IEEE Trans. Med. Imag., vol. 10, no. 3, pp. 473-478, Sep. 1991.
15. D. Fraser, "Interpolation by the FFT revisited. An experimental investigation," IEEE Trans. Acoust. Speech Signal Process., vol. 37, no. 5, pp. 665-676, May 1989.
16. S. Basu and Y. Bresler, "Error analysis and performance optimization of fast hierarchical hackprojection algorithms," IEEE Trans. Image Process., vol. 10, no. 7, pp. 1103-1117, Jul 2001.
17. [17[ J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, "Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction," IEEE Trans. Med. Imag., vol. 16, no. 2, pp. 166-175, Apr. 1997.
18. P. M. Joseph and R. D. Spital, "The exponential edge-gradient effect in X-ray computed tomography," Phys. Med. Biol. vol. 26, no. 3, pp. 473-187, May 1981.
19. B. De Man and S. Basu, "Distance-driven projection and backprojection in three dimensions," Phys. Med. Biol., vol. 49, no. 11, pp. 2463-2475, Jun 2004.
20. J. A. Fessler and W. L. Rogers, "Spatial resolution properties of penalized-likelihood image reconstruction methods: space-invariant tomographs," IEEE Trans. Image Process., vol. 5, no. 9, pp. 1346-1358, Sep. 1996.
21. J. A. Fessler and S. D. Booth, "Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction," IEEE Trans. Image Process., vol. 8, no. 5, pp. 688-699, May 1999.
22. K. Sauer and C. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Process., vol. 41, no. 2, pp. 534-548, Feb. 1993.
23. J. A. Fessler, Matlab Tomography Toolbox 2004 [Online], Available: http://www.eecs.umich.edu/~fessler
24. A. Averbuch and Y. Shkolnisky, "3D Fourier based discrete Radon transform," Appl. Computational Harmonic Anal., vol. 15, no. 1, pp. 33-69, Jul. 2003.
25. W. Lawton, "A new polar Fourier transform for computer-aided tomography and spotlight synthetic aperture radar," IEEE Trans. Acoust. Speech Signal Process., vol. 36, no. 6, pp. 931-933, Jun. 1988.
26. P. L. Bellon and S. Lanzavecchia, "Fast direct Fourier methods, based on one- and two-pass coordinate transformations, yield accurate reconstructions of X-ray CT clinical images," Phys. Med. Biol., vol. 42, no. 3, pp. 443-464, Mar. 1997.
27. J. Waidén, "Analysis of the direct Fourier method for computer tomography," IEEE Trans. Med. Imag., vol. 19, no. 3, pp. 211-222, Mar. 2000.
28. D. Potts and G. Steidl, "A new linogram algorithm for computerized tomography," IMA J. Numer. Anal., vol. 21, no. 3, pp. 769-782, Jul. 2001.
29. [29[ G, Bal and P. Moireau, "Fast numerical inversion of the attenuated Radon transform with full and partial measurements," Inverse Prob., vol. 20, no. 4, pp. 1137-1164, Aug. 2004.
30. 2 log N) native fan-beam tomographic reconstruction," in Proc. IEEE Int. Symp. Biomedical Imaging, 2002, pp. 824-827.