Fractional Radon Transform and its Convolution Theorem

  • Saleem Iqbal Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Hazrat Ali Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Farhana Sarwar Department of Mathematics F.G.Girls Degree College, Madrissa Road , Quetta, Cantt, 87300, Pakistan
  • Abdul Rehman Abdul Rehman Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Saboor Ahmed Kakar Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
Keywords: Radon transform, Fractional Radon transform, Fourier transform, Fractional Fourier transform

Abstract

Fractional Radon transform which is symbolized with the notation , it is different to the classical Radon transform. The shift property of fractional Radon transform is controlled by the fractional order Rotation of the input object at angle  will rotate the fractional Radon transform at that angle thus, the fractional Radon transform is rotation invariant. The fractional Fourier transform, with respect to  of the fractional Radon transform of an object is the central slice at angle  of the -dimensional fractional Fourier transform of this object. In this paper we explain the mathematical formation of fractional Radon transform and established a convolution theorem for the fractional Radon transform.

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Published
2019-11-03
Section
Articles