Numerische Mathematik

, Volume 32, Issue 4, pp 431–438 | Cite as

On the inversion of the attenuated Radon transform

  • Frank Natterer
Article

Abstract

We given an inversion formula for the attenuated Radon transform
$$\bar \omega _L $$
for constant attenuation μ which is accurate up toO(µ4)

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

Subject Classifications

AMS(MOS) 65R05 CR 5.18 

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References

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    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 1977Google Scholar
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    Ludwig, D.: The Radon Transform on Euclidean Space. Comm. Pure Appl. Math.19, 49–81 (1966)Google Scholar
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    Kneser, H.: Funktionentheorie. Göttingen 1958Google Scholar
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    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover 1972Google Scholar
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    Budinger, T.F., Gullberg, G.T.: Three-Dimensional Reconstruction in Nuclear Medicine Emission Immaging. IEEE Transactions on Nuclear Science21, 2–20 (1974)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Frank Natterer
    • 1
  1. 1.Angewandte mathematik und InformatikFachbereich 10 der Universität des SaarlandesSaarbrückenGermany (Fed. Republic)

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