Skip to main content
SpringerLink
Log in
Book cover

Poisson Point Processes pp 109–145Cite as

Tomographic Imaging

  • Chapter
  • First Online:

  • 2267 Accesses

Abstract

PPP methods for tomographic imaging are presented in this chapter. The primary emphasis is on methods for emission tomography, but transmission tomography is also included. The famous Shepp-Vardi algorithm for positron emission tomography (PET) is obtained via the EM method for time-of-flight data. Single-photon emission computed tomography (SPECT) is used in practice much more often than PET. It differs from PET in many ways, yet the models and the mathematics of the two methods are similar. (Both PET and SPECT are also closely related to multitarget tracking problems discussed in Chapter 6.) Transmission tomography is the final topic discussed. The Lange-Carson algorithm is derived via the EM method. CRBs for unbiased estimators for emission and transmission tomography are discussed. Regularization and Grenander’s method of sieves are reviewed in the last section.

There are a thousand thousand reasons to live this life, every one of them sufficient.

Marilynne Robinson, Gilead, 2004

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. A. H. Delaney and Y. Bresler. A fast and accurate iterative reconstruction algorithm for parallel-beam tomography. IEEE Transactions on Image Processing, IP-5(5):740–753, 1996.

    Article  Google Scholar 

  2. C. L. Epstein. Introduction to the Mathematics of Medical Imaging. SIAM Press, Philadelphia, PA, second edition, 2007.

    Google Scholar 

  3. J. A. Fessler. Statistical image reconstruction methods for transmission tomography. In M. Sonka and J. M. Fitzpatrick, editors, Handbook of Medical Imaging, SPIE, Bellingham, Washington, volume 2, pages 1–70, 2000.

    Google Scholar 

  4. A. O. Hero and J. A. Fessler. A fast recursive algorithm for computing CR-type bounds for image reconstruction problems. In Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference, Orlando, FL, pages 1188–1190, 1992.

    Google Scholar 

  5. A. O. Hero and J. A. Fessler. A recursive algorithm for computing Cramér-rao-type bounds on estimator variance. IEEE Transactions on Information Theory, IT-40:843–848, 1994.

    MathSciNet  Google Scholar 

  6. K. Lange and R. Carson. EM reconstruction algorithms for emission and transmission tomography. Journal of Computer Assisted Tomography, 8(2):306–316, 1984.

    Google Scholar 

  7. J. Langner. Development of a parallel computing optimized head movement correction method in positron emission tomography. Master’s thesis, University of Applied Sciences Dresden and Research Center, Dresden-Rossendorf, 2003. http://www.jens-langner.de/ftp/MScThesis.pdf.

  8. R. M. Lewitt and S. Matej. Overview of methods for image reconstruction from projections in emission computed tomography. Proceedings of the IEEE, 91(10):1588–1611, 2003.

    Article  Google Scholar 

  9. M. I. Miller, D. L. Snyder, and T. R. Miller. Maximum-likelihood reconstruction for single-photon emission computed-tomography. IEEE Transactions on Nuclear Science, NS-32(1):769–778, 1985.

    Article  Google Scholar 

  10. J. A. O’Sullivan and J. Benac. Alternating minimization algorithms for transmission tomography. IEEE Transactions on Medical Imaging, MI-26:283–297, 2007.

    Article  Google Scholar 

  11. L. A. Shepp and Y. Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Transactions on Medical Imaging, MI-1(2):113–122, 1982.

    Article  Google Scholar 

  12. D. L. Snyder and M. I. Miller. Random Point Processes in Time and Space. Springer, New York, Second edition, 1991.

    Book  MATH  Google Scholar 

  13. M. Ter-Pogossian. The Physical Aspects of Diagnostic Radiology. Hoeber Medical Division, Harper and Rowe, New York, 1967.

    Google Scholar 

  14. Y. Watanabe. Derivation of linear attenuation coefficients from CT numbers for low-energy photons. Physics in Medicine Biology, 44:2201–2211, 1999.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Metron Inc., 1818 Library St, Reston, Virginia, 20190-6281, USA

    Roy L. Streit

Authors
  1. Roy L. Streit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roy L. Streit .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Streit, R.L. (2010). Tomographic Imaging. In: Poisson Point Processes. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6923-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-6923-1_5

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-6922-4

  • Online ISBN: 978-1-4419-6923-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation