The Radon Transform in ℝ2. The Distributions Used as a Tool for its Inversion in Circular Decomposition and Elimination of an Additive Noise. Systematic Tables of Transforms

  • L. R. Oudin
Conference paper
Part of the Lecture Notes in Medical Informatics book series (LNMED, volume 8)

Summary

The Radon Transform ℛ θ [f] of a continuous function f with compact support is reminded. Next, the transform ℛ θ[T] of a temperate distribution is expressed in a new definition. Choosing distributions of rapid descent, a generalization of the properties found for classical Radon images of square integrable functions with compact support is evidenced. Namely two distributions are used in order to find the analytical correspondence between the circular harmonics of a function f and their respective images by ℛ θ. The use of distributions leads to four classes of applications:
  1. 1)

    Restitution of circular harmonics from Radon image; its advantages.

     
  2. 2)

    Compatibility conditions upon circular harmonics.

     
  3. 3)

    Algorithmic processes for elimination of an additive noise.

     
  4. 4)

    Convolution between distributions. Applications.

     
Finally a Table of systematic Radon is built and digitized inversion matrix is deduced.

Keywords

Fast Fourier Transform Compact Support Additive Noise Compatibility Condition Radon Transform 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Bibliography

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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • L. R. Oudin
    • 1
  1. 1.French-German Research InstituteSaint-LouisFrance

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