Abstract

In this paper a novel fractional transformation for which we coin the term the fractional Radon transform is defined. This transform generalizes the Radon transform and combines it with the fractional Fourier transform. Both transformations are useful tools for invariant pattern recognition, tomography, and signal processing. Some of the properties of the new transformation, as well as further directions for investigation, are presented.

© 1996 Optical Society of America

Optical illustration of a varied fractional Fourier-transform order and the Radon–Wigner display

David Mendlovic, Rainer G. Dorsch, Adolf W. Lohmann, Zeev Zalevsky, and Carlos Ferreira
Appl. Opt. 35(20) 3925-3929 (1996)

Relationships between the Radon–Wigner and fractional Fourier transforms

Adolf W. Lohmann and Bernard H. Soffer
J. Opt. Soc. Am. A 11(6) 1798-1801 (1994)

Optical realization of the radon transform

Tali Ilovitsh, Asaf Ilovitsh, John Sheridan, and Zeev Zalevsky
Opt. Express 22(26) 32301-32307 (2014)

New signal representation based on the fractional Fourier transform: definitions

David Mendlovic, Zeev Zalevsky, Rainer G. Dorsch, Yigal Bitran, Adolf W. Lohmann, and Haldun Ozaktas
J. Opt. Soc. Am. A 12(11) 2424-2431 (1995)

Invariant pattern recognition, symmetry, and Radon transforms

David A. Pintsov
J. Opt. Soc. Am. A 6(10) 1544-1554 (1989)