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The Attenuated Radon Transform

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Book cover Mathematics and Computer Science in Medical Imaging

Part of the book series: NATO ASI Series ((NATO ASI F,volume 39))

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Abstract

The attenuated Radon transform comes up in single particle emission computed tomography (SPECT). We describe some mathematical properties of the attenuated Radon transform and line out numerical procedures using the conjugate gradient algorithm. In the case of constant attenuation, a complete solution is possible, including the attenuation correction problem. We conclude with a suggestion for the attenuation correction problem in the general case.

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References

  • Barrett, H.H. (1987). Fundamentals of the Radon transform. These proceedings.

    Google Scholar 

  • Budinger, T.F., Gullberg, G.T., and Huesman, R.H. (1979). Emission computed tomography. In: Image Reconstruction from Projections, G.T. Herman (ed.), Springer-Verlag, Berlin, pp. 147–246.

    Google Scholar 

  • Heike, U. (1986). Single-photon emission computed tomography by inverting the attenuated Radon transform with least-squares collocation, Inverse problems2, pp. 307–330.

    Article  MATH  MathSciNet  Google Scholar 

  • Hertle, A. (1986). The identification problem for the constantly attenuated Radon transform. Preprint, Fachbereich Mathematik, Universitât Mainz.

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  • Luenberger, D.G. (1973). Introduction to ‘linear and nonlinear programming, Addison-Wesley, Reading.

    MATH  Google Scholar 

  • Markoe, A. (1987). Fourier inversion of the attenuated Radon transform, SIAM J. Math. Anal., to appear.

    Google Scholar 

  • Natterer, F. (1979). On the inversion of the attenuated Radon transform, Numer. Math.32, pp. 431–438.

    Article  MATH  MathSciNet  Google Scholar 

  • Natterer, F. (1983). Computerized tomography with unknown sources, SIAM J. Appl. Math.43, pp. 1201–1212.

    Article  MATH  MathSciNet  Google Scholar 

  • Natterer, F. (1986). The mathematics of computerized tomography, Wiley-Teubner, Stuttg art.

    MATH  Google Scholar 

  • Natterer, F. (1987). Regularization techniques in medical imaging. These proceedings.

    Google Scholar 

  • Tretiak, O. and Metz, C. (1980). The exponential Radon transform, SIAM J. Appl. Math.39, pp. 341–354.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Universität Münster, West Germany

    Frank Natterer

Authors
  1. Frank Natterer
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ, Delft, The Netherlands

    Max A. Viergever (Director) (Director)

  2. Department of Medical Physics, University College London, Gower Street, WC1E 6BT, London, UK

    Andrew Todd-Pokropek (Director) (Director)

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© 1988 Springer-Verlag Berlin Heidelberg

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Natterer, F. (1988). The Attenuated Radon Transform. In: Viergever, M.A., Todd-Pokropek, A. (eds) Mathematics and Computer Science in Medical Imaging. NATO ASI Series, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83306-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-83306-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83308-3

  • Online ISBN: 978-3-642-83306-9

  • eBook Packages: Springer Book Archive

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