Skip to main content

Abstract

For a given function f defined in the plane, which may represent, for instance, the attenuation-coefficient function in a cross section of a sample, the fundamental question of image reconstruction calls on us to consider the value of the integral of f along a typical line \(\,\ell_{t,\,\theta }\). For each pair of values of t and \(\,\theta\), we will integrate f along a different line.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 64.99
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

Institutional subscriptions

Bibliography

  1. Deans, S.R.: The Radon Transform and Some of Its Applications. Krieger, Malabar (1993); reprinted by Dover, Mineola (2007)

    Google Scholar 

  2. Helgason, S.: The Radon Transform, 2nd edn. Birkhäuser, Boston (1999)

    Book  MATH  Google Scholar 

  3. Kuchment, P.: The Radon Transform and Medical Imaging. CBMS, vol. 85. SIAM, Philadelphia (2014)

    Google Scholar 

  4. Natterer, F.: The Mathematics of Computerized Tomography. Classics in Applied Mathematics, vol. 32. SIAM, Philadelphia (2001)

    Google Scholar 

  5. Radon, J.: Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisserMannigfaltigkeiten. Berichte Sächsische Akademie der Wissenschaften 69, 262–277 (1917)

    Google Scholar 

  6. Shepp, L.A., Logan, B.F.: The Fourier reconstruction of a head section. IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

2.1 Electronic Supplementary Material

Below is the link to the electronic supplementary material.

Feeman2E_Rcode (9 kb)

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Feeman, T.G. (2015). The Radon Transform. In: The Mathematics of Medical Imaging. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-22665-1_2

Download citation

Publish with us

Policies and ethics