Data Acquisition and Image Reconstruction for 3D PET

  • Michel Defrise
  • Paul Kinahan
Part of the Developments in Nuclear Medicine book series (DNUM, volume 32)


The purpose of this chapter is to explain the underlying concepts of the most common image reconstruction methods. The question to be answered in this chapter is: how can we use the additional information from a 3D PET scan (as compared to a 2D scan) to improve the signal to noise ratio in the reconstructed image?


Image Reconstruction Projection Data Ramp Filter Image Reconstruction Method Complete Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Badawi RD, Marsden PK, Cronin BF, Sutcliffe JL, Maisey MN. Optimization of noise-equivalent count rates in 3D PET. Phys Med Biol 1997; 41: 1755–1776.CrossRefGoogle Scholar
  2. Barrett HH, Swindell W. Radiological Imaging. New York: Academic Press, 1981.Google Scholar
  3. Barrett HH, Wilson DW, Tsui BMW. Noise properties of the EM algorithm: I. Theory. Phys Med Biol 1994; 39: 833–846.CrossRefGoogle Scholar
  4. Cheung WK, Lewitt RM. Modified Fourier reconstruction method using shifted transform samples. Phys Med Biol 1991; 36: 269–277.PubMedCrossRefGoogle Scholar
  5. Colsher JG. Fully three-dimensional positron emission tomography. Phys Med Biol 1980; 25: 103–115.PubMedCrossRefGoogle Scholar
  6. Cutler PD, Xu M. Strategies to improve 3D whole body PET image reconstruction. J Nuc Med 1995; 36: 93–94.Google Scholar
  7. Daube-Witherspoon ME, Muehllehner G. Treatment of axial data in three-dimensional PET. J Nuc Med 1987; 28: 1717–1724.Google Scholar
  8. Deans SR. The Radon transform and some of its applications. New York: Wiley, 1983.Google Scholar
  9. Defrise M, Geissbuhler A, Townsend DW. Performance study of 3D reconstruction algorithms for PET. Phys Med Biol 1994; 39.Google Scholar
  10. Defrise M, Kinahan PE, Townsend DW, Michel C, Sibomana M, Newport D. Exact and approximate rebinning algorithms for 3D PET data. IEEE Trans Med Imag 1997; 16: 145–158.CrossRefGoogle Scholar
  11. Defrise M, Townsend DW, Clack R. FaVoR: A fast reconstruction algorithm for volume imaging in PET. Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference; 1991 November 2–9; Santa Fe, NM;1919–1923.Google Scholar
  12. Defrise M, Townsend DW, Deconinck F. Statistical noise in three-dimensional positron tomography. Phys Med Biol 1990; 35: 131–138.CrossRefGoogle Scholar
  13. Edholm PR, Lewitt RM, Lindholm B. Novel Properties of the Fourier Decomposition of the Sinogram. Proceedings of the International Workshop on Physics and Engineering of Computerized Multidimensional Imaging and Processing; 1986; Proceedings of the SPIE 671: 8–18.CrossRefGoogle Scholar
  14. Egger M. Fast Volume reconstruction in positron emission tomography. [PhD Thesis]. Laussane, University of Laussane, 1996.Google Scholar
  15. Fessier JA. Penalized weighted least squares image reconstruction for positron emission tomography. IEEE Trans Med Imag 1994; 13 (2): 290–300.CrossRefGoogle Scholar
  16. Furuie SS, Herman GT, Narayan TK, Kinahan PE, Karp JS, Lewitt RM, Matej S. A methodology for testing for statistically significant differences between fully 3D PET reconstruction algorithms. Phys Med Biol 1994; 39: 341–354.PubMedCrossRefGoogle Scholar
  17. Hudson H, Larkin R. Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans Med Imag 1994; 13: 601–609.CrossRefGoogle Scholar
  18. Herbert T, Leahy RM. A generalized EM algorithm for 3-D Bayesian reconstruction for Poisson data using Gibbs priors. IEEE Trans Med Imag 1989;MI-8:194–202.Google Scholar
  19. Jackson JI, Meyer CH, Nishimura DG, Macovski A. Selection of a convolution function for Fourier inversion using gridding. IEEE Trans Med Imag 1991; 10: 473–478.CrossRefGoogle Scholar
  20. Johnson CA, Yan Y, Carson RE, Martino RL, Daube-Witherspoon ME. A system for the 3D reconstruction of retracted-septa data using the EM algorithm. IEEE Trans Nuc Sci 1995; 42: 1223–1227.CrossRefGoogle Scholar
  21. Kak AC, Slaney M. Principles of Computerized Tomographic Imaging. New York: IEEE Press, 1988.Google Scholar
  22. Kinahan PE, Karp JS. Figures of Merit for comparing reconstruction algorithms with a volume-imaging PET scanner. Phys Med Biol 1994; 39: 631–638.PubMedCrossRefGoogle Scholar
  23. Kinahan PE, Michel C, Defrise M, Townsend DW, Sibomana M, Lonneux M, Newport DF, Luketich JD. Fast Iterative Image Reconstruction of 3D PET Data. Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference; 1996 November 5–8; Anaheim, CA; 1918–1922.Google Scholar
  24. Kinahan PE, Rogers JG. Analytic 3D image reconstruction using all detected events. IEEE Trans Nuc Sci 1989; 36: 964–968.CrossRefGoogle Scholar
  25. Lewitt RM, Muehllehner G, Karp JS. Three-dimensional image reconstruction for PET by multi-slice rebinning and axial image filtering. Phys Med Biol 1994; 39: 321–339.CrossRefGoogle Scholar
  26. Liow J-S, Strother SC, Rehm K, Rottenburg A. Improved resolution for PET volume-imaging through three-dimensional iterative reconstruction. J Nuc Med 1997; 38: 1623 1630.Google Scholar
  27. Matej S, Herman GT, Narayan TK, Furuie SS, Lewitt RM, Kinahan PE. Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms. Phys Med Biol 1994; 39: 355–367.PubMedCrossRefGoogle Scholar
  28. Matej S, Karp JS, Lewitt RM, Becher AJ. Performance of the Fourier Rebinning Algorithm for PET with Large Acceptance Angles. Phys Med Biol 1998; 43.Google Scholar
  29. Natterer F. The Mathematics of Computerized Tomography. New York: Wiley, 1986.Google Scholar
  30. Orlov SS. Theory of three-dimensional image reconstruction: I Conditions for a complete set of projections. Soviet Physics Crystallography 1976; 20: 429–433.Google Scholar
  31. Orlov SS. Theory of three-dimensional image reconstruction: II The recovery operator. Soviet Physics Crystallography 1976; 20: 429–433.Google Scholar
  32. Qi J, Leahy RM, Cherry SR, Chatziioannou A, Farquhar TH. High Resolution 3D Bayesian Image Reconstruction Using the Small Animal microPET Scanner. Phys Med Biol 1998; 43.Google Scholar
  33. Shepp LA, Vardi Y. Maximum likelihood reconstruction for emission tomography. IEEE Trans Med Imag 1982; 2: 113–119.CrossRefGoogle Scholar
  34. Sossi V, Stazyk M, Kinahan PE, Ruth T. Implementation of a 3D acquisition and 2D reconstruction technique on an ECAT 953B for phantom and human basal ganglia studies. J Comp Assist Tomogr 1994; 18: 1004–1010.CrossRefGoogle Scholar
  35. Stearns CW, Chesler DA, Brownell GL. Accelerated image reconstruction for a cylindrical positron tomograph using Fourier domain methods. IEEE Trans Nuc Sci 1990; 37: 773–777.CrossRefGoogle Scholar
  36. Stearns CW, Crawford CR, Hu H. Oversampled filters for quantitative volumetric PET reconstruction. Phys Med Biol 1994; 39: 381–388.PubMedCrossRefGoogle Scholar
  37. Townsend DW, Defrise M. Image reconstruction methods in positron tomography. CERN;Technical Report. 1993.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Michel Defrise
    • 1
  • Paul Kinahan
    • 2
  1. 1.Division of Nuclear MedicineFree University of Brussels (VUB)Belgium
  2. 2.PET Facility, Department of RadiologyUniversity of PittsburghUSA

Personalised recommendations