Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transformations

  • Imants Svalbe
  • Shekhar Chandra
  • Andrew Kingston
  • Jean-Pierre Guédon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


A quantum mechanics based method is presented to generate sets of digital angles that may be well suited to describe projections on discrete grids. The resulting angle sets are an alternative to those derived using the Farey fractions from number theory. The Farey angles arise naturally through the definitions of the Mojette and Finite Radon Transforms. Often a subset of the Farey angles needs to be selected when reconstructing images from a limited number of views. The digital angles that result from the quantisation of angular momentum (QAM) vectors may provide an alternative way to select angle subsets. This paper seeks first to identify the important properties of digital angles sets and second to demonstrate that the QAM vectors are indeed a candidate set that fulfils these requirements. Of particular note is the rare occurrence of degeneracy in the QAM angles, particularly for the half-integral angular momenta angle sets.


Discrete projection tomography digital angles finite Radon transforms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Imants Svalbe
    • 1
  • Shekhar Chandra
    • 1
  • Andrew Kingston
    • 2
  • Jean-Pierre Guédon
    • 2
  1. 1.School of PhysicsMonash UniversityAustralia
  2. 2.IRCCyN-IVCÉcole polytechnique de l’Université de NantesFrance

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