Fractional Hartley Transform and its Inverse
Main Article Content
The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.
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Alieva T, Lopez V, Agullo-Lopez F, Almeida LB. The fractional Fourier transform in optical propagation problems. J Mod Opt. 1994; 41(5): 1037-1044. http://dx.doi.org/10.1080/09500349414550971.
Gaikwad V, Chaudhary MS. n-dimensional fractional Fourier transform. Bull Cal Math Soc. 2016; 108(5): 375-390. https://www.researchgate.net/publication/368309310_n-dimensional_fractional_Fourier_transform.
Yu SS, Zhou NR, Gong LH, Nie Z. Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system. Opt Lasers Eng. 2020; 124: 105816. http://dx.doi.org/10.1016/j.optlaseng.2019.105816.
Pei SC, Tseng CC, Yeh MH, Ding JJ. A new definition of continuous fractional Hartley transform. International Conference on Acoustics, speech, and signal processing, IEEE. 1998; 3: 1485-1488. http://ntur.lib.ntu.edu.tw/bitstream/246246/2007041910021806/1/00681730.pdf.
Roopkumar R, Ganesan C. Fractional Hartley transform on G-Boehmian space. Bol Soc paran Mat. 2022; 40: 1-11. http://dx.doi.org/10.5269/bspm.43828.
Yadav AK., Singh P, Singh K. Cryptosystem based on devil’s vortex Fresnel lens in the fractional Hartley domain. J Opt. 2018; 47(2): 208–219. https://link.springer.com/article/10.1007/s12596-017-0435-9.
Singh P, Yadav AK., Singh K, Saini I. Asymmetric watermarking scheme in fractional Hartley domain using modified equal modulus decomposition. J Optoelectron Adv Mater. 2019; 21(7–8): 484–491. https://joam.inoe.ro/articles/asymmetric-watermarking-scheme-in-fractional-hartley-domain-using-modified-equal-modulus-decomposition/fulltext.
Yadav AK, Singh P, Saini I, Singh K. Asymmetric encryption algorithm for colour images based on fractional Hartley transform. J Mod Opt. 2019; 66(6): 629–642. https://doi.org/10.1080/09500340.2018.1559951.
Ye HS, Zhou NR, Gong LH. Multi-image compression-encryption scheme based on quaternion discrete fractional Hartley transform and improved pixel adaptive diffusion. Signal Process. 2020; 175: 107652. http://dx.doi.org/10.1016/j.sigpro.2020.107652.
Kumar J, Singh P, Yadav AK. Asymmetric double-image encryption using twin decomposition in fractional Hartley domain. Opt Appl. 2022; 52(1): 21-35. http://dx.doi.org/10.37190/oa220102.
Rimani R, Said NH, Ali-Pacha A, Ramos JAL. An efficient image encryption using a dynamic nonlinear and secret diffusion scheme. Baghdad Sci J. 2021; 18(3): 628-639. http://dx.doi.org/10.21123/bsj.2021.18.3.0628.
Hamza YA, Tewfiq NE, Ahmed MQ. An enhanced approach of image steganographic using discrete Shearlet transform and secret sharing. Baghdad Sci J. 2022; 19(1): 197-207. http://dx.doi.org/10.21123/bsj.2022.19.1.0197.