# Fractional Radon Transform and its Convolution Theorem

## 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.

## References

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

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*American Scientific Research Journal for Engineering, Technology, and Sciences*,

*61*(1), 7–12. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/5301

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