A Discrete Modulo N Projective Radon Transform for N × N Images

  • Andrew Kingston
  • Imants Svalbe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)


This paper presents a Discrete Radon Transform (DRT) based on congruent mathematics that applies to N × N arrays where \(N \in \mathcal{N}\). This definition incorporates and is a natural extension of the more restricted cases of the finite Radon transform [1] where N must be prime, the discrete periodic Radon transform [2] where N must be a power of 2, and the DRT over p n [3], where N must be a power of a single prime. The DRT exactly and invertibly maps a 2-D image to a set of 1-D projections of length N. Projections are found as the sum of the pixels centred on a parallel set of discrete lines. The image is assumed to be periodic and these lines wrap around the array under modulo N arithmetic. Properties of the continuous Radon transform are preserved in the DRT; a discrete form of the Fourier slice theorem applies, as does the convolution property. A formula is given to find the projection set required to be exactly invertible for arrays with N any composite number, as well as a means to determine the level of redundancy in sampling that is introduced on such composite arrays.


Discrete Form Inversion Process Projection Angle Radon Transform Short Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrew Kingston
    • 1
  • Imants Svalbe
    • 1
  1. 1.Centre for X-ray Physics and Imaging, School of Physics and Materials EngineeringMonash UniversityAUS

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