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Multiple-parameter fractional quaternion Fourier transform and its application in colour image encryption

Multiple-parameter fractional quaternion Fourier transform and its application in colour image encryption

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In this study, by using the quaternion algebra, multiple-parameter fractional quaternion Fourier transform (MPFrQFT) is proposed to generalise the conventional multiple-parameter fractional Fourier transform (MPFrFT) to quaternion signal processing in a holistic manner. First, the new transform MPFrQFT and its inverse transform are defined. An efficient discrete implementation method of MPFrQFT is then proposed, in which the relationship between MPFrQFT and MPFrFT of four components is utilised for a quaternion signal. Finally, a new colour image encryption algorithm based on the proposed MPFrQFT and the double random phase encoding technique is proposed to evaluate the performance of the proposed MPFrQFT. Experimental results demonstrate that: (i) the computational time of the proposed implementation method is almost a half of the direct method's time; (ii) the proposed MPFrQFT-based encryption algorithm has an overall better performance than eight compared algorithms in security test and robustness test: it is more secure than the compared frequency-based algorithms due to the larger key space and the more sensitive key ‘transform orders’; it is also more robust than the compared spatial-domain algorithms.

References

    1. 1)
      • 1. Ell, T.A., Sangwine, S.J.: ‘Hypercomplex Fourier transforms of color images’, IEEE Trans. Image Process., 2007, 16, (1), pp. 2235.
    2. 2)
      • 2. Hitzer, E.: ‘General two-sided quaternion Fourier transform, convolution and Mustard convolution’, Adv. Appl. Clifford Algebras, 2016, 27, (1), pp. 115.
    3. 3)
      • 3. Chen, B.J., Coatrieux, G., Chen, G., et al: ‘Full 4-D quaternion discrete Fourier transform based watermarking for color images’, Digit. Signal Process., 2014, 28, (5), pp. 106119.
    4. 4)
      • 4. Chan, W.L., Choi, H., Baraniuk, G.: ‘Directional hypercomplex wavelets for multidimensional signal analysis and processing’. Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, Montreal, Canada, 2004, pp. 996999.
    5. 5)
      • 5. Gai, S.: ‘New banknote defect detection algorithm using quaternion wavelet transform’, Neurocomputing, 2016, 196, pp. 133139.
    6. 6)
      • 6. Guo, L.Q., Dai, M., Zhu, M.: ‘Multifocus color image fusion based on quaternion curvelet transform’, Opt. Express, 2012, 20, (17), pp. 1884618860.
    7. 7)
      • 7. Li, Y.N.: ‘Quaternion polar harmonic transforms for color images’, IEEE Signal Process. Lett., 2013, 20, (8), pp. 803806.
    8. 8)
      • 8. Chen, B.J., Qi, X.M., Sun, X.M., et al: ‘Quaternion pseudo-Zernike moments combining both of RGB information and depth information for color image splicing detection’, J. Vis. Commun. Image Represent., 2017, 49, pp. 283290.
    9. 9)
      • 9. Wang, X.Y., Li, W.Y., Yang, H.Y., et al: ‘Invariant quaternion radial harmonic Fourier moments for color image retrieval’, Opt. Laser Technol., 2015, 66, pp. 7888.
    10. 10)
      • 10. Feng, W., Hu, B.: ‘Quaternion discrete cosine transform and its application in color template matching’. Proc. 1st Int. Cong. Image and Signal Processing (CISP 2008), Sanya, China, 2008, pp. 252256.
    11. 11)
      • 11. Xu, G.L., Wang, X.T., Xu, X.G.: ‘Fractional quaternion Fourier transform, convolution and correlation’, Signal Process., 2008, 88, (10), pp. 25112517.
    12. 12)
      • 12. Wei, D.Y., Li, Y.M.: ‘Different forms of Plancherel theorem for fractional quaternion Fourier transform’, Optik, 2013, 124, (24), pp. 69997002.
    13. 13)
      • 13. Roopkumar, R.: ‘Quaternionic one-dimensional fractional Fourier transform’, Optik-Int. J. Light Electron Opt., 2016, 127, (24), pp. 1165711661.
    14. 14)
      • 14. Shao, Z.H., Wu, J.S., Coatrieux, J.L., et al: ‘Quaternion gyrator transform and its application to color image encryption’. Proc. 2013 20th IEEE Int. Conf. Image Processing (ICIP), Melbourne, Australia, 2013, pp. 45794582.
    15. 15)
      • 15. Yu, C.Y., Li, J.Z., Li, X., et al: ‘Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram’, Multimedia Tools Appl., 2017, 77, (4), pp. 45854608.
    16. 16)
      • 16. Chen, B.J., Yang, J.H., Jeon, B., et al: ‘Kernel quaternion principal component analysis and its application in RGB-D object recognition’, Neurocomputing, 2017, 266, pp. 293303.
    17. 17)
      • 17. Ortolani, F., Comminiello, D., Scarpiniti, M., et al: ‘Frequency domain quaternion adaptive filters: algorithms and convergence performance’, Signal Process., 2017, 136, pp. 6980.
    18. 18)
      • 18. Zhang, D., Meng, D., Han, J.: ‘Co-saliency detection via a self-paced multiple-instance learning framework’, IEEE Trans. Pattern Anal. Mach. Intell., 2017, 39, (5), pp. 865878.
    19. 19)
      • 19. Wang, J.W., Li, T., Shi, Y.Q., et al: ‘Forensics feature analysis in quaternion wavelet domain for distinguishing photographic images and computer graphics’, Multimedia Tools Appl., 2016, 76, (22), pp. 2372123737.
    20. 20)
      • 20. Chen, B.J., Zhou, C.F., Jeon, B., et al: ‘Quaternion discrete fractional random transform for color image adaptive watermarking’, Multimedia Tools Appl., 2018, 77, (16), pp. 2080920837.
    21. 21)
      • 21. Namias, V.: ‘The fractional order Fourier transform and its application to quantum mechanics’, J. Inst. Math. Appl., 1980, 25, pp. 241265.
    22. 22)
      • 22. Yuan, L., Ran, Q.W., Zhao, T.Y.: ‘Image authentication based on double-image encryption and partial phase decryption in nonseparable fractional Fourier domain’, Opt. Laser Technol., 2017, 88, pp. 111120.
    23. 23)
      • 23. Pei, S.C., Yeh, M.H.: ‘The discrete fractional cosine and sine transforms’, IEEE Trans. Signal Process., 2001, 49, (6), pp. 11981207.
    24. 24)
      • 24. Pei, S.C., Ding, J.J.: ‘Fractional cosine, sine, and Hartley transforms’, IEEE Trans. Signal Process., 2002, 50, (7), pp. 16611680.
    25. 25)
      • 25. Lohmann, A.W., Mendlovic, D., Zalevsky, Z.: ‘Fractional Hilbert transform’, Opt. Lett., 1996, 21, (4), pp. 281283.
    26. 26)
      • 26. Mendlovic, D., Zalevsky, Z., Mas, D., et al: ‘Fractional wavelet transform’, Appl. Opt., 1997, 36, (20), pp. 48014806.
    27. 27)
      • 27. Liu, Z.J., Zhao, H.F., Liu, S.T.: ‘A discrete fractional random transform’, Opt. Commun., 2005, 255, (4), pp. 357365.
    28. 28)
      • 28. Zhou, N.R., Li, H.L., Wang, D., et al: ‘Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform’, Opt. Commun., 2015, 343, pp. 1021.
    29. 29)
      • 29. Zhang, Y., Gu, B.Y., Dong, B.Z., et al: ‘Fractional Gabor transform’, Opt. Lett., 1997, 22, (21), pp. 15831585.
    30. 30)
      • 30. Wang, Y.Q., Peng, Z.M.: ‘The optimal fractional S transform of seismic signal based on the normalized second-order central moment’, J. Appl. Geophys., 2016, 129, pp. 816.
    31. 31)
      • 31. Dou, J.Y., He, Q., Peng, Y., et al: ‘A convolution-based fractional transform’, Opt. Quantum Electron., 2016, 48, (8), doi: 10.1007/s11082-016-0685-9.
    32. 32)
      • 32. Lang, J., Tao, R., Ran, Q. W., et al: ‘The multiple-parameter fractional Fourier transform’, Sci. China F, Inf. Sci., 2008, 51, (8), pp. 10101024.
    33. 33)
      • 33. Lang, J., Tao, R., Wang, Y.: ‘The discrete multiple-parameter fractional Fourier transform’, Sci. China, Inf. Sci., 2010, 53, (11), pp. 22872299.
    34. 34)
      • 34. Ran, Q.W., Zhang, H.Y., Zhang, J., et al: ‘Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform’, Opt. Lett., 2009, 34, (11), pp. 17291731.
    35. 35)
      • 35. Shan, M., Chang, J., Zhong, Z., et al: ‘Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps’, Opt. Commun., 2012, 285, (21), pp. 42274234.
    36. 36)
      • 36. Pareek, N.K., Patidar, V., Sud, K.K.: ‘Image encryption using chaotic logistic map’, Image Vis. Comput., 2006, 24, (9), pp. 926934.
    37. 37)
      • 37. Bhatnagar, G., Wu, Q.M.J.: ‘Selective image encryption based on pixels of interest and singular value decomposition’, Digit. Signal Process., 2012, 22, (4), pp. 648663.
    38. 38)
      • 38. Refregier, P., Javidi, B.: ‘Optical image encryption based on input plane and Fourier plane random encoding’, Opt. Lett., 1995, 20, (7), pp. 767769.
    39. 39)
      • 39. Wang, X., Zhai, H., Li, Z., et al: ‘Double random-phase encryption based on discrete quaternion Fourier-transforms’, Optik, 2011, 122, (20), pp. 18561859.
    40. 40)
      • 40. Lee, I.H., Cho, M.: ‘Double random phase encryption based orthogonal encoding technique for color images’, J. Opt. Soc. Korea, 2014, 18, (2), pp. 129133.
    41. 41)
      • 41. Huang, H.Q., Yang, S.Z.: ‘Colour image encryption based on logistic mapping and double random-phase encoding’, IET Image Process., 2017, 11, (4), pp. 211216.
    42. 42)
      • 42. Unnikrishnan, G, Joseph, J, Singh, K.: ‘Optical encryption by double-random phase encoding in the fractional Fourier domain’, Opt. Lett., 2000, 25, (12), pp. 887889.
    43. 43)
      • 43. Liu, Z., Liu, S.: ‘Double image encryption based on iterative fractional Fourier transform’, Opt. Commun., 2007, 275, (2), pp. 324329.
    44. 44)
      • 44. Kumar, P., Joseph, J., Singh, K.: ‘Double random phase encryption with in-plane rotation of a modified Lohmann's second-type system in the anamorphic fractional Fourier domain’, Opt. Eng., 2008, 47, (11), p. 117001.
    45. 45)
      • 45. Tao, R., Lang, J., Wang, Y.: ‘Optical image encryption based on the multiple-parameter fractional Fourier transform’, Opt. Lett., 2008, 33, (6), pp. 581583.
    46. 46)
      • 46. Yang, Y.G., Xia, J., Jia, X., et al: ‘Novel image encryption/decryption based on quantum Fourier transform and double phase encoding’, Quantum Inf. Process., 2013, 12, (11), pp. 34773493.
    47. 47)
      • 47. Subakan, O.N., Vemuri, B.C.: ‘A quaternion framework for color image smoothing and segmentation’, Int. J. Comput. Vis., 2011, 91, (3), pp. 233250.
    48. 48)
      • 48. Hua, Z.Y., Zhou, Y.C.: ‘Design of image cipher using block-based scrambling and image filtering’, Inf. Sci., 2017, 396, pp. 97113.
    49. 49)
      • 49. Zhou, Y.C., Panetta, K., Agaian, S., et al: ‘Image encryption using P-Fibonacci transform and decomposition’, Opt. Commun., 2012, 285, (5), pp. 594608.
    50. 50)
      • 50. Hua, Z.Y., Zhou, Y.C.: ‘Image encryption using 2D Logistic-adjusted-Sine map’, Inf. Sci., 2016, 339, pp. 237253.
    51. 51)
      • 51. Hua, Z.Y., Yi, S., Zhou, Y.C.: ‘Medical image encryption using high-speed scrambling and pixel adaptive diffusion’, Signal Process., 2018, 144, pp. 134144.
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