A 3-D filtered-backprojection reconstruction algorithm for combined parallel- and cone-beam SPECT data

  • Chunwu Wu
  • Miles N. Wernick
  • Chin-Tu Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 687)


Cone-beam (cb) collimation for single-photon emission computed tomography (spect) provides higher sensitivity than parallel-hole collimation, however it produces truncated projection data that can lead to undesirable image artifacts. In response, it has been suggested (Jaszczak 1992) that parallel-beam and cone-beam data be combined to obtain increased sensitivity while maintaining completeness of the data for accurate reconstruction. Herein, a 3-d filtered-backprojection (fbp) approach for reconstructing such data sets is proposed. The algorithm begins with a rebinning of the parallel- and cone-beam (p&cb) data to a common planeintegral projection space: the projection space of the 3-d Radon transform. A normalization step is then implemented to correct for the sampling pattern of the system, thus assuring that the rebinned data are proportional to the plane integrals of the source distribution of the object. Finally, a fully 3-D fbp reconstruction based on the inversion formula of the 3-Radon transform is performed using the rebinned plane integrals. The advantage of this algorithm is that, by making the necessary corrections prior to reconstruction, it avoids residual artifacts that can remain after other methods are employed. In addition, the computation time required by the proposed method is substantially shorter than that reported for maximum-likelihood reconstructions by the expectation-maximization (em) algorithm (Jaszczak 1992).


3-D reconstruction 3-D Radon transform cone beam parallel beam single-photon emission computed tomography 


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  1. Barrett HH (1984). The Radon transform and its applications. in: Progress in Optics XXI, edited by E Wolf, Elsevier Science Publishers, New York, 1984, pp. 217–286.Google Scholar
  2. Clack R, Zeng GL, Weng Y Christian PE and Gullberg GT. (1991). Cone beam single photon emission computed tomography using two orbits. In: Information Processing in Medical Imaging, XIIth IPMI International Conference, Kent, England, July 6–14. Eds: A. Colchester and D Hawkes, Springer-Verlag, New York, 1991, pp. 45–54.Google Scholar
  3. Deans SR (1983). The Radon transform and some of its applications. John Wiley & Sons, New York, 1983.Google Scholar
  4. Feldkamp LA, Davis LC, and Kress JW (1984). Practical cone-beam algorithm. J. Opt. Soc. Am. A 1:612–619.Google Scholar
  5. Grangeat P, Le Masson P, Melennec P and Sire P (1991). Evaluation of the 3D Radon transform algorithm for cone beam reconstruction. SPIE 1445: 320–331.CrossRefGoogle Scholar
  6. Gullberg GT, Zeng GL, Datz FL, Christian PE, Tung CH and Morgan HT (1992). Review of convergent beam tomography in single photon emission computed tomography. Phys. Med. Biol. 37: 507–534.CrossRefPubMedGoogle Scholar
  7. Herman GT (1980). Image Reconstructions From Projections: The Fundamentals of Computerized Tomography, Academic Press, New York.Google Scholar
  8. Jaszczak RJ, Chang LT, Stein NA and Moore FE (1979). Whole-body single-photon emission computed tomography using dual, large-field-of-view scintillation cameras. Phys. Med. Biol. 24: 1123–1143.CrossRefPubMedGoogle Scholar
  9. Jaszczak RJ, Floyd CE, Manglos SH, Greer KL and Coleman RE (1986a). Three-dimensional single photon emission computed tomography using cone beam collimation (CB-SPECT). Proc. SPIE 671: 193–199.Google Scholar
  10. Jaszczak RJ, Floyd CE, Manglos SH, Greer KL and Coleman RE (1986b). Cone beam collimation for single photon emission computed tomography: analysis, simulation and image reconstruction using filtered backprojection. Med. Phys. 13: 484–489.CrossRefPubMedGoogle Scholar
  11. Jaszczak RJ, Li J, Wang H and Coleman RE (1992). Three-dimensional SPECT reconstruction of combined cone beam and parallel beam data. Phys. Med. Biol. 37: 535–548.CrossRefPubMedGoogle Scholar
  12. Lim CB, Chang LT and Jaszczak RJ (1980). Performance analysis of three camera configuration for single photon emission tomography. IEEE Trans. Nucl. Sci. NS-77: 559–568.Google Scholar
  13. Lim CB, Gottschalk S, Walker R, Schreiner R et al (1985). Triangular SPECT system for 3-D total organ volume imaging: Design concept and preliminary imaging results. IEEE Trans. Nucl. Sci. NS-32: 741–747.Google Scholar
  14. Manglos SH, Jaszczak RJ and Greer KL (1989). Cone beam SPECT reconstruction with camera tilt. Phys. Med. Biol. 34: 625–631.CrossRefPubMedGoogle Scholar
  15. Shepp LA (1980). Computerized tomography and nuclear magnetic resonance. J. of Comput. Assist. Tomog. 4: 94–107.Google Scholar
  16. Smith BD (1985). Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods,” IEEE Trans. Med. Imaging M14: 14–25.Google Scholar
  17. Stazyk MW, Rogers JG, and Harrop R (1992). Full data utilization in PVI using the 3D Radon transform. Phys. Med. Biol. 37: 689–704.CrossRefPubMedGoogle Scholar
  18. Tuy HK (1983). An inversion formula for cone-beam reconstruction. SIAM J. Appl. Math. 43:546–552.CrossRefGoogle Scholar
  19. Wu C, Chen CT, Gunter DL and Ordonez CE (1992). Fully 3-D PET reconstruction with plane integrals. Radiology (supplement) 185 (P): 252 (abstract).Google Scholar
  20. Zeng GL and Gullberg GT (1990). A study of reconstruction artifacts in cone beam tomography using filtered backprojection and iterative EM algorithms. IEEE Trans. Nucl. Sci. NS-37: 759–765.CrossRefGoogle Scholar
  21. Zheng GL and Gullberg GT (1992). A cone-beam tomography algorithm for orthogonal circle-and-line orbit. Phys. Med. Biol. 37: 563–578.CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Chunwu Wu
    • 1
  • Miles N. Wernick
    • 1
  • Chin-Tu Chen
    • 1
  1. 1.Frank Center for Image Analysis, Franklin McLean Memorial Research Institute, Department of RadiologyThe University of ChicagoChicago

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