Skip to main content
Log in

On the inversion of the attenuated Radon transform

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Abstract

We given an inversion formula for the attenuated Radon transform

$$\bar \omega _L $$

for constant attenuation μ which is accurate up toO(µ 4)

We also derive an integral equation of the second kind for the solution ofR μf=g. The implementation of both methods for the inversion ofR μ consists basically of a generalized filtered backprojection algorithm. Numerical examples are presented.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Budinger, T.F., Gullberg, G.T.: Transverse Section Reconstruction, of Gamma-Ray Emitting Radionuclides in Patients. In: Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine. (M.M. Ter-Pogossian et al., ed.) Baltimore: University Park Press 1977

    Google Scholar 

  2. Ludwig, D.: The Radon Transform on Euclidean Space. Comm. Pure Appl. Math.19, 49–81 (1966)

    Google Scholar 

  3. Kneser, H.: Funktionentheorie. Göttingen 1958

  4. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover 1972

  5. Budinger, T.F., Gullberg, G.T.: Three-Dimensional Reconstruction in Nuclear Medicine Emission Immaging. IEEE Transactions on Nuclear Science21, 2–20 (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Natterer, F. On the inversion of the attenuated Radon transform. Numer. Math. 32, 431–438 (1979). https://doi.org/10.1007/BF01401046

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01401046

Subject Classifications

Navigation