Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain

We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.

[1]  Zhengjun Liu,et al.  Double image encryption based on iterative fractional Fourier transform , 2007 .

[2]  Z. Zalevsky,et al.  The Fractional Fourier Transform: with Applications in Optics and Signal Processing , 2001 .

[3]  E.J. Candes.  Compressive Sampling , 2022 .

[4]  Bo Wang,et al.  Optical image encryption based on interference. , 2008, Optics letters.

[5]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[6]  Seiichi Uchida,et al.  A parallel image encryption method based on compressive sensing , 2012, Multimedia Tools and Applications.

[7]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[8]  G. Sharma,et al.  On the security and robustness of encryption via compressed sensing , 2008, MILCOM 2008 - 2008 IEEE Military Communications Conference.

[9]  Yang Li,et al.  Optical image encryption technique based on compressed sensing and Arnold transformation , 2013 .

[10]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[11]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[12]  Colin J. R. Sheppard,et al.  Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution , 2012 .

[13]  Linfei Chen,et al.  Optical image encryption with redefined fractional Hartley transform , 2008 .

[14]  Xiaoli Xu,et al.  Application of Compressed Sensing for Secure Image Coding , 2010, WASA.

[15]  Jingjuan Zhang,et al.  Multiple-image encryption by wavelength multiplexing. , 2005, Optics letters.

[16]  Ran Tao,et al.  Optical image encryption based on the multiple-parameter fractional Fourier transform. , 2008, Optics letters.

[17]  G. Unnikrishnan,et al.  Optical encryption by double-random phase encoding in the fractional Fourier domain. , 2000, Optics letters.

[18]  A. Lohmann.  Image rotation, Wigner rotation, and the fractional Fourier transform , 1993 .

[19]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[20]  Min Gao,et al.  A robust image encryption scheme over wireless channels , 2009, 2009 International Conference on Wireless Communications & Signal Processing.

[21]  Lu-Zhong Cai,et al.  Information security system by iterative multiple-phase retrieval and pixel random permutation. , 2006, Applied optics.

[22]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[23]  Danhua Liu,et al.  A Robust Image Transmission Scheme for Wireless Channels Based on Compressive Sensing , 2010, ICIC.

[24]  B Javidi,et al.  Optical image encryption based on input plane and Fourier plane random encoding. , 1995, Optics letters.

[25]  Narendra Singh,et al.  Optical image encryption using fractional Fourier transform and chaos , 2008 .