Author Affiliations
1Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China2Key Laboratory of Modern Imaging and Displaying Technology, Anhui University, Hefei 230039, Chinashow less
Fig. 1. Schematic diagram of compressive color holography
Fig. 2. Schematic setup of multiple color image encryption based on space division multiplexing
Fig. 3. Decryption model of multiple color image
Fig. 4. Flow chart of the proposed multiple color image encryption and decryption process
Fig. 5. Comparison of self-sparse color image with inherent noise
Fig. 6. Comparison of complex color image with inherent noise
Fig. 7. Comparison of self-sparse color image with encryption
Fig. 8. Comparison of complex color image with encryption
Fig. 9. The simulated results of encryption and decryption security on RPM
Fig. 10. The simulated results of encryption and decryption security on propagating distance
Fig. 11. The simulated results to investigate the robustness against occlusion attack (sampling ratio δ)
Fig. 12. Simulated results on the robust of decryption against Gaussian noise with the different standard deviation σ
Variable | Description | Dimensions | fc | The c channel of vectorized multiple color images | (Nx·Ny·L)×1 | R | Diagonal matrix of RPMs | (Nx·Ny·L)×(Nx·Ny·L) | B | Block diagonal matrix composed of multiple 2Ddiscrete fourier transform (DFT) matrix | (Nx·Ny·L)×(Nx·Ny·L) | \begin{document}$\mathit{\pmb{\mathscr{F}}}$\end{document}2D | 2D DFT matrix | (Nx·Ny)×(Nx·Ny) | \begin{document}$\mathit{\pmb{\mathscr{F}}}$\end{document}2D-1 | 2D inverse DFT matrix | (Nx·Ny)×(Nx·Ny) | Ql, c | PSF of the c channel of l color image | (Nx·Ny)×(Nx·Ny) | Qc | PSF of the c channel of multiple color images | (Nx·Ny)×(Nx·Ny·L) | gc | Thec channel of vectorized encrypted color hologram | (Nx·Ny)×1 | g | Vectorization of encrypted color hologram | (Nx·Ny)×3 |
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Table 1. Definition of variables and description of dimensions
| Inherent noise reconstruction | Un-inherent noise reconstruction | | SNR | PSNR | NC | SNR | PSNR | NC | “A” | 54.844 | 67.546 | 0.998 | 59.419 | 71.504 | 0.998 | “H” | 57.571 | 70.276 | 0.998 | 60.999 | 73.251 | 0.998 | “T” | 57.580 | 72.527 | 0.998 | 61.002 | 75.573 | 0.998 | “V” | 57.116 | 70.527 | 0.998 | 59.009 | 72.171 | 0.998 | “lena” | 21.903 | 24.337 | 0.948 8 | 27.612 | 28.990 | 0.992 | “house” | 19.684 | 23.091 | 0.940 5 | 24.650 | 27.231 | 0.988 | “airplane” | 24.426 | 23.641 | 0.959 | 30.388 | 28.438 | 0.995 | “peppers” | 20.672 | 24.002 5 | 0.944 7 | 27.114 | 29.343 | 0.990 |
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Table 2. The performance comparison of color image with inherent noise
| Unencrypted reconstruction | Encrypted reconstruction | | SNR | PSNR | NC | SNR | PSNR | NC | “A” | 33.043 | 48.594 | 0.974 | 59.419 | 71.504 | 0.998 | “H” | 34.663 | 50.375 | 0.975 | 61.000 | 73.251 | 0.998 | “T” | 36.835 | 54.582 | 0.981 | 61.002 | 75.573 | 0.998 | “V” | 36.070 | 52.246 | 0.977 | 59.009 | 72.171 | 0.998 |
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Table 3. The performance comparison of multiple self-sparse color image
| Unencrypted reconstruction | Encrypted reconstruction | | SNR | PSNR | NC | SNR | PSNR | NC | “lena” | 10.821 | 14.406 | 0.803 | 27.611 | 28.990 | 0.992 | “house” | 11.096 | 15.459 | 0.846 | 24.650 | 27.231 | 0.988 | “airplane” | 7.952 | 8.909 | 0.557 | 30.388 | 28.438 | 0.995 | “peppers” | 8.703 | 13.352 | 0.810 | 27.114 | 29.343 | 0.990 |
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Table 4. The performance comparison of multiple complex color image shown
| 75% | 50% | 20% | 10% | Avg_SNR | 24.922 | 22.783 | 19.595 | 16.688 | Avg_PSNR | 26.315 | 24.445 | 21.697 | 19.151 | Avg_NC | 0.986 | 0.977 | 0.966 | 0.944 |
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Table 5. The performance comparison of occlusion attack
| 0.1 | 0.2 | 0.3 | 0.4 | Avg_SNR | 22.960 | 19.551 | 17.062 | 15.079 | Avg_PSNR | 25.738 | 24.131 | 24.207 | 23.463 | Avg_NC | 0.987 | 0.985 | 0.977 | 0.974 |
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Table 6. The robust performance comparison of decryption under Gaussian noise