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


Radon transform, Fractional Radon transform, Fourier transform, Fractional Fourier transform


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.


S.R. Deans. The Radon Transform and Some of Its appications . John Wiley & Sons, Inc. (1983)

H.M. Zalevsky , D. Mendlovic . Fractional Wiener Filter. Applied Optics. Vol, 35. No, 20, (1996), 3930-3935.

H.M. Zalevsky , D. Mendlovic. Fractional Radon transform: definition. Applied Optics , Vol. 35, No 23,

(1996), 4628-4630

Y. Hong, J. Hua. (2003). Fractional Radon Transform and Transform of winger Operator. Commun. Theor. Phys Vol. 39, No 2, (2003), 147-150.

V. Namias. The fractional order Fourier transform and its application to quantum mechanics, IMA Journal of Applied Mathematics, 25(3) (1980) 241-265

D. Mendlovic & H.M.. Ozaktas. Fractiona Fourier transforms and their Optical implementation: J. Opt. Soc. Am. A. Vol. 10, No. 9, (1993), 1875-1880.

M.G. Raymer, D.T. Smithey, et al . spatial and temporal Optical field reconstruction using phase space tomography; Quantum optics . Vol.77, (1994), (1994)245-253

R.G. Dorsch, A.W. Lohmann, Y. Bitran, D. Mendlovic and H.M.Ozaktas. Chirp filtering in the fractiona Fourier domain . Appl. Opt. 33, (1994). 7599-7602.

H.M. Ozaktas, B.Barshan,D. Mendlovic, & L.Onural. Convolution, filtering and multiplexing in the fractional Foureir domain and their relation to chirp and wavelet transform . J, Opt. Soc. Am A11, (1994). 547-559

L.B. Almeida, “The fractional Fourier transform and time-frequency representations”, IEEE Transactions on Signal Processing, 42(11) (1994) 3084–3091,

V.Parot, C.Sing-Long, et al. (2012). Application of the Fractional Fourier Transform to image reconstruction in MRI. Magn Reson Med 68(1), 17-29.

N. Goel & K.Singh. Modified correlation theorem for the linear canonical transform with representatation transformation in quntum mechanics . Signal Image Video process., (2014). 595-601.

L.B. Almeida A Product and convolution theorems for the fractional Fourier transform. IEEE, signal process. Lett. 5(4), (1998), 101-103




How to Cite

Iqbal, S., Ali, H. ., Sarwar, F., Abdul Rehman, A. . R., & Kakar, S. A. . (2019). Fractional Radon Transform and its Convolution Theorem. American Scientific Research Journal for Engineering, Technology, and Sciences, 61(1), 7–12. Retrieved from