The Property of Frequency Shift in 2D-FRFT Domain With Application to Image Encryption

The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is shown that the magnitude of image reconstruction from phase information is frequency shift-invariant in 2D-FRFT domain, enhancing the robustness of image encryption, an important multimedia security task. Experiments are conducted to demonstrate the effectiveness of this property against the frequency shift attack, improving the robustness of image encryption.

[1]  Ran Tao,et al.  Optimized sparse fractional Fourier transform: Principle and performance analysis , 2020, Signal Process..

[2]  R. Tao,et al.  Fractional Power Spectrum and Fractional Correlation Estimations for Nonuniform Sampling , 2020, IEEE Signal Processing Letters.

[3]  Xuejing Kang,et al.  Color Image Encryption Using Pixel Scrambling Operator and Reality-Preserving MPFRHT , 2019, IEEE Transactions on Circuits and Systems for Video Technology.

[4]  Anlong Ming,et al.  Reality-Preserving Multiple Parameter Discrete Fractional Angular Transform and Its Application to Color Image Encryption , 2019, IEEE Transactions on Circuits and Systems for Video Technology.

[5]  Jin Hu,et al.  Anamorphic fractional Fourier transforms graded index lens designed using transformation optics. , 2018, Optics express.

[6]  Kuldip K. Paliwal,et al.  Reconstruction of a Signal from the Real Part of Its Discrete Fourier Transform [Tips & Tricks] , 2018, IEEE Signal Processing Magazine.

[7]  Peijia Zheng,et al.  Efficient Encrypted Images Filtering and Transform Coding With Walsh-Hadamard Transform and Parallelization , 2018, IEEE Transactions on Image Processing.

[8]  Ahmet Serbes,et al.  Compact Fractional Fourier Domains , 2017, IEEE Signal Processing Letters.

[9]  Ran Tao,et al.  Multichannel Random Discrete Fractional Fourier Transform , 2015, IEEE Signal Processing Letters.

[10]  Byung-Geun Lee,et al.  Implementing compressive fractional Fourier transformation with iterative kernel steering regression in double random phase encoding , 2014 .

[11]  L. Guan,et al.  Rotation Invariance in 2D-FRFT with Application to Digital Image Watermarking , 2013, Journal of Signal Processing Systems.

[12]  Lei Gao,et al.  The spatial shift operations on image reconstruction from 2D-FRFT information with application to SAR moving target detection , 2013, 2013 IEEE China Summit and International Conference on Signal and Information Processing.

[13]  Patrick Flandrin,et al.  On Phase-Magnitude Relationships in the Short-Time Fourier Transform , 2012, IEEE Signal Processing Letters.

[14]  V. M. Kuz’kin,et al.  Frequency shifts of sound field maxima in oceanic waveguides , 2011 .

[15]  Naitong Zhang,et al.  Multichannel Sampling and Reconstruction of Bandlimited Signals in Fractional Fourier Domain , 2010, IEEE Signal Processing Letters.

[16]  V. M. Kuz’kin,et al.  Methods of measuring frequency shifts in the interference structure of the sound field in oceanic waveguides , 2010 .

[17]  V. M. Kuz’kin,et al.  Frequency shifts of the spatial interference structure of the sound field in shallow water , 2008 .

[18]  Mariano Rivera,et al.  Half-quadratic cost function for computing arbitrary phase shifts and phase: Adaptive out of step phase shifting. , 2006, Optics express.

[19]  John T. Sheridan,et al.  Fractional Fourier transform-based image encryption: phase retrieval algorithm , 2003 .

[20]  M. L. Calvo,et al.  Image reconstruction from amplitude-only and phase-only data in the fractional Fourier domain , 2003 .

[21]  M. L. Calvo,et al.  Importance of the phase and amplitude in the fractional Fourier domain. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  Soo-Chang Pei,et al.  Relations between fractional operations and time-frequency distributions, and their applications , 2001, IEEE Trans. Signal Process..

[23]  Soo-Chang Pei,et al.  Two dimensional discrete fractional Fourier transform , 1998, Signal Process..

[24]  A.I. Zayed,et al.  A convolution and product theorem for the fractional Fourier transform , 1998, IEEE Signal Processing Letters.

[25]  A. Zayed.  On the relationship between the Fourier and fractional Fourier transforms , 1996, IEEE Signal Processing Letters.

[26]  M. Hayes.  The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform , 1982 .

[27]  V. Namias.  The Fractional Order Fourier Transform and its Application to Quantum Mechanics , 1980 .

[28]  Zhou Min.  Digital Computation of Fractional Fourier Transform , 2002 .

[29]  F. H. Kerr,et al.  On Namias's fractional Fourier transforms , 1987 .