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SCIENTIA SINICA Informationis, Volume 47 , Issue 6 : 736(2017) https://doi.org/10.1360/N112016-00241

Privacy-preserving encrypted image fusion algorithm for remote sensing

More info
  • ReceivedOct 9, 2016
  • AcceptedNov 28, 2016
  • PublishedMar 6, 2017

Abstract


Funded by

国家自然科学基金(61602039,61272512,61300177)

北京市自然科学基金(4164098,4121001)

  • Figure 1

    (Color online) Examples of remote sensing images. (a) Panchromatic image; (b) multi-spectral image

  • Figure 2

    Flow chart of principal component analysis transformation method

  • Figure 3

    (Color online) Privacy-preserving image fusion system model

  • Figure 10

    (Color online) Fusion image obtained by decryption

  • Figure 13

    (Color online) Algorithm execution time with varying iterations

  • Figure 14

    (Color online) Correlation between adjacent pixels in encrypted image with different iterations

  • Figure 17

    (Color online) Examples illustrating decryption with incorrect and correct keys. (a) $x_0=0.10000001$;protectłinebreak (b) $x_0=0.63278099$; (c) $x_0=0.63278101$; (d) correct key $x_0$

  • Figure 18

    (Color online) Example illustrating encrypted images under attacks and their corresponding decrypted images. (a) Shear attack encrypted image; (b) decrypted image of (a); (c) noise attack encrypted image; (d) decrypted image of (c)

  • Table 1   Quantitative comparison of image fusion results
    Image Mean Standard Information Average Correlation
    deviation entropy gradient coefficient
    Original multi-spectral image 103.495 57.2562 6.398 13.103
    Fusion image with PCA 98.371 49.492 6.673 14.685 0.7565
    Fusion image with SecureFusion 98.371 49.492 6.673 14.685 0.7565
  • Table 2   Statistical analysis of the encrypted image with varying keys
    StatisticOriginal Key $x_0$
    image 0.000010.0001 0.001 0.01 0.1 0.3 0.5 0.7 0.9
    Horizontal 0.9275 $-$0.0121$-$0.0086 $-$0.0111$-$0.0128$-$0.0132$-$0.0058$-$0.0032 $-$0.0069 $-$0.0133
    correlation
    Vertical 0.9099 0.00017$-$0.00038$-$0.000190.000180.00120.00170.00180.00064 0.00057
    correlation
    Right opposite 0.8561 $-$0.00031$-$0.00029 0.00010 $-$0.0017$-$0.00110.00032 $-$0.000076 0.00041$-$0.0022
    angles correlation
    Left opposite 0.877 0.000570.00039 0.000220.000850.00016$-$0.00099$-$0.001 0.00140.00065
    angles correlation
    Average 521.4309520.9178 521.5568521.2322521.0533 521.1658 521.5278521.2874521.3996
    move distance
    Fixed point 0.0000010 0 0 0.000002 0 0.000001 0.000001 0.000001
    percentage
  • Table 3   Quantitative comparison of image fusion results
    Image Mean Standard Informatio Average Correlation
    deviation entropy gradient coefficient
    Fusion image without attack 98.371 49.492 6.673 14.685 0.7565
    Fusion image with shear attack 86.600 56.739 6.250 10.077 0.587
    Fusion image with noise attack 99.847 50.738 6.622 16.541 0.699