Fig. 1. Datagram format
Fig. 2. Principle of interference and vector decomposition
Fig. 3. Minimized interference
Fig. 4. Reversible information hiding embedding process with multi-image interference
Fig. 5. Extraction process of multi-image interference reversible information hiding
Fig. 6. Reversible information hiding theory of multiple images
Fig. 7. Embedding and Restore
Fig. 8. Embedded image and histogram
Fig. 9. PSNR of restore contains secret images with different carriers at different embedding rates
Fig. 10. Results of reduction multiple analysis
Fig. 11. Quantitative analysis results
Fig. 12. Robust analysis results
Fig. 13. Add noise reduction renderings
Image | Animal | Barbara | Monarch | Cameraman | Baboon | Restore image | Restore contains secret images |
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PSNR/dB | inf | inf | inf | inf | inf | inf | 42.050 057 | SSIM | 1 | 1 | 1 | 1 | 1 | 1 | 0.982 350 |
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Table 1. PSNR and SSIM of images at each stage
Carrier images | Encryption image | Insert 16 bpp | Insert 32 bpp | Insert 64 bpp | Insert 128 bpp | Insert 512 bpp |
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7.445 5 | 7.042 8 | 7.040 6 | 7.036 3 | 7.041 2 | 7.039 8 | 7.046 5 |
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Table 2. Information entropy of ciphertext images and embedded images at different embedding rates
Embedding rate | Restore hidden image (PSNR/SSIM) | Restore image (PSNR/SSIM) | Restore contains secret images (PSNR/SSIM) |
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16 bpp | inf/1.0 | inf/1.0 | 52.201 1 dB/0.997 7 | 32 bpp | inf/1.0 | inf/1.0 | 47.613 4 dB/0.993 5 | 64 bpp | inf/1.0 | inf/1.0 | 40.997 1 dB/0.971 7 | 128 bpp | inf/1.0 | inf/1.0 | 33.831 3 dB/0.883 9 | 512 bpp | inf/1.0 | inf/1.0 | 27.105 6 dB/0.663 8 |
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Table 3. PSNR and SSIM of each restored image at different embedding rates
Carrier images | Embedding rate/bpp | PNSR/dB |
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Literature [7] | Literature [8] | Literature [11] | Literature [12] | This Paper | Literature [7] | Literature [8] | Literature [11] | Literature [12] | This Paper |
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Average | 1.063 6 | 0.5 | 1.615 8 | 8 | 32 | 47.49 | 41.84 | 45.78 | 35.46 | 48.02 | Lena | 1.412 2 | 0.5 | 1.985 3 | 8 | 32 | 46.12 | 46.37 | 44.19 | 35.86 | 47.61 | Airplane | 1.696 5 | 0.5 | 2.318 4 | 8 | 32 | 43.27 | 46.45 | 41.09 | 35.18 | 47.29 | Barbara | 0.855 5 | 0.5 | 1.457 4 | 8 | 32 | 49.85 | 40.22 | 45.31 | 35.32 | 48.53 | Baboon | 0.290 2 | 0.5 | 0.581 0 | 8 | 32 | 56.42 | 29.74 | 53.49 | 35.49 | 47.05 | Man | 1.387 4 | 0.5 | 1.734 2 | 8 | 32 | 45.43 | 44.86 | 45.23 | 35.47 | 48.44 | Cameraman | 1.641 9 | 0.5 | 1.618 3 | 8 | 32 | 43.84 | 43.42 | 45.36 | 35.43 | 49.21 |
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Table 4. Comparison of the maximum embedding rate of different algorithms and PSNR of restore contains secret images
Crop | Can reconstruct | Gaussian noise | Can reconstruct | Salt & pepper noise | Can reconstruct |
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200×200(Not cut to check area) | Yes | 0.001 | Yes | 0.01 | Yes | 400×400(Not cut to check area) | Yes | 0.002 | Yes | 0.1 | Yes | 99×99(Cut to check area) | Yes | 0.003 | Yes | 0.25 | Yes | 100×100(Cut to check area) | No | 0.004 | No | 0.26 | No |
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Table 5. Robust analysis results of multi-image datagram reconstruction
Embedding rate | Carrier owner | Information hider | Hidden information receiver | Carrier receiver |
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16 bpp | 0.496 7 | 0.213 4 | 0.746 0 | 0.807 8 | 32 bpp | 0.496 9 | 0.442 8 | 1.492 0 | 1.555 8 | 64 bpp | 0.495 7 | 0.849 7 | 2.930 1 | 2.996 9 | 128 bpp | 0.496 6 | 1.655 5 | 5.883 2 | 5.947 1 | 512 bpp | 0.497 6 | 3.298 1 | 11.708 6 | 11.771 5 |
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Table 6. Time spent by each owner at different embedding rates(s)