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An optical image watermarking method based on computational ghost imaging and multiple logistic maps

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Abstract

An optical watermarking method is presented based on computational ghost imaging and multiple logistic maps. Instead of directly embedding an original watermark into the host image, the object image considered as the watermark is encoded to a series of bucket values using computational ghost imaging in the beginning. The host image is decomposed into four components using a single-level discrete wavelet transform. Then, all or part of bucket values is fused with the low-frequency coefficients of the host image. After applying the corresponding inverse wavelet transform, the watermarked host image can be obtained with high imperceptibility. In this process, a sequence generated with a logistic map is used to scramble bucket values, and another sequence is used to randomly select the fusion positions in the low-frequency component. In this way, the security level of the proposed method can be greatly enhanced when initial values and bifurcation parameters of multiple logistic maps are considered secret keys. Optical experiments are performed to verify the validity of the proposed watermarking method and the robustness resisting against various attacks such as noise and occlusion attack.

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References

  1. P. Refregier, B. Javidi, Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995)

    Article  ADS  Google Scholar 

  2. A. Alfalou, C. Brosseau, Recent advances in optical image processing. Progr. Opt. 60, 119–262 (2015)

    Article  Google Scholar 

  3. B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M.S. Millán, N.K. Nishchal, R. Torroba, J.F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J.T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P.W.H. Pinkse, A.P. Mosk, A. Markman, Roadmap on optical security. J. Opt. 18(8), 083001 (2016)

    Article  ADS  Google Scholar 

  4. M. Khurana, H. Singh, Two level phase retrieval in fractional Hartley domain for secure image encryption and authentication using digital signatures. Multimed. Tools Appl. 79, 13967–13986 (2020)

    Article  Google Scholar 

  5. A. Fatima, N.K. Nishchal, Image authentication using a vector beam with sparse phase information. J. Opt. Soc. Am. A 35(6), 1053–1062 (2018)

    Article  ADS  Google Scholar 

  6. I. Moon, F. Yi, M. Han, J. Lee, Efficient asymmetric image authentication schemes based on photon counting-double random phase encoding and RSA algorithms. Appl. Opt. 55(16), 4328–4335 (2016)

    Article  ADS  Google Scholar 

  7. Y. Qin, Z. Wang, H. Wang, Q. Gong, N. Zhou, Robust information encryption diffractive-imaging-based scheme with special phase retrieval algorithm for a customized data container. Opt. Lasers Eng. 105, 118–124 (2018)

    Article  Google Scholar 

  8. Z. Shao, Y. Tang, M. Liang, Y. Shang, F. Wang, Y. Wang, Double image encryption based on symmetry of 2D-DFT and equal modulus decomposition. Multimed. Tools Appl. 80, 8973–8998 (2021)

    Article  Google Scholar 

  9. M.R. Abuturab, Asymmetric multiple information cryptosystem based on chaotic spiral phase mask and random spectrum decomposition. Opt. Laser Technol. 98, 298–308 (2018)

    Article  ADS  Google Scholar 

  10. X. Li, M. Zhao, Y. Xing, L. Li, S.T. Kim, X. Zhou, Q.H. Wang, Optical encryption via monospectral integral imaging. Opt. Express. 25(25), 31516–31527 (2017)

    Article  ADS  Google Scholar 

  11. P.W.M. Tsang, Single-random-phase holographic encryption of images. Opt. Lasers Eng. 89, 22–28 (2017)

    Article  Google Scholar 

  12. L. Zhang, Z. Zhang, H. Ye, K. Yi, Multi-image holographic encryption based on phase recovery algorithm and ghost imaging. Appl. Phys. B 126, 136 (2020)

    ADS  Google Scholar 

  13. L. Sui, Y. Cheng, Z. Wang, A. Tian, A. Asundi, Single-pixel correlated imaging with high-quality reconstruction using iterative phase retrieval algorithm. Opt. Lasers Eng. 111, 108–113 (2018)

    Article  Google Scholar 

  14. T. Zhao, Y. Chi, Hierarchical visual cryptography for multisecret images based on a modified phase retrieval algorithm. Multimed. Tools Appl. 79, 12165–12181 (2020)

    Article  Google Scholar 

  15. L. Sui, X. Zhao, C. Huang, A. Tian, A. Asundi, An optical multiple-image authentication based on transport of intensity equation. Opt. Lasers Eng. 116, 116–124 (2019)

    Article  Google Scholar 

  16. L. Sui, L. Zhang, Q. Wang, A. Tian, A. Asundi, Multiple-image authentication based on the single-pixel correlated imaging and multiple-level wavelet transform. Opt. Lasers Eng. 130, 106102 (2020)

    Article  Google Scholar 

  17. L. Sui, X. Zhang, C. Huang, A. Tian, A. Asundi, Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms. Opt. Lasers Eng. 113, 29–37 (2019)

    Article  Google Scholar 

  18. T. Zhao, Q. Ran, L. Yuan, Y. Chi, J. Ma, Security of image encryption scheme based on multi-parameter fractional Fourier transform. Opt. Commun. 376, 47–51 (2016)

    Article  ADS  Google Scholar 

  19. K. Jin, T. Lai, Y. Qi et al., Efficient coherent detection of maneuvering targets based on location rotation transform and non-uniform fast Fourier transform. Front. Inform. Technol. Electron. Eng. 21, 1251–1266 (2020)

    Article  Google Scholar 

  20. X. Li, X. Meng, Y. Wang, X. Yang, Y. Yin, X. Peng, W. He, G. Dong, H. Chen, Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain. Opt. Lasers Eng. 96, 7–16 (2017)

    Article  Google Scholar 

  21. H. Anshula, Singh: Security-enrichment of an asymmetric optical image encryption-based devil’s vortex Fresnel lens phase mask and lower upper decomposition with partial pivoting in gyrator transform domain. Opt Quant Electron 53, 204 (2021)

    Article  Google Scholar 

  22. N. Zhou, H. Li, D. Wang, S. Pan, Z. Zhou, Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt. Commun. 343, 10–21 (2015)

    Article  ADS  Google Scholar 

  23. L. Sui, Z. Bei, Z. Wang, A. Tian, An optical color image watermarking scheme by using compressive sensing with human visual characteristics in gyrator domain. Opt. Lasers Eng. 92, 85–93 (2017)

    Google Scholar 

  24. X. Sun, Z. Shao, Y. Shang et al., Multiple-image encryption based on cascaded gyrator transforms and high-dimensional chaotic system. Multimed. Tools Appl. 80, 15825–15848 (2021)

    Article  Google Scholar 

  25. H. Anshula, Singh: Cryptanalysis for double-image encryption using the DTLM in frequency plane with QR decomposition and gyrator transform. Opt. Rev. 28, 596–610 (2021)

    Article  Google Scholar 

  26. Y. Xiong, A. He, C. Quan, Hybrid attack on an optical cryptosystem based on phase-truncated Fourier transforms and a random amplitude mask. Appl. Opt. 57(21), 6010–6016 (2018)

    Article  ADS  Google Scholar 

  27. J. Wu, Z. Xie, Z. Liu, W. Liu, Y. Zhang, S. Liu, Multiple-image encryption based on computational ghost imaging. Opt. Commun. 359, 38–43 (2016)

    Article  ADS  Google Scholar 

  28. L. Zhang, Z. Pan, L. Wu, X. Ma, High-performance compression and double cryptography based on compressive ghost imaging with the fast Fourier transform. Opt. Lasers Eng. 86, 329–337 (2016)

    Article  Google Scholar 

  29. X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, H. Chen, Multiple-image encryption based on compressive ghost imaging and coordinate sampling. IEEE Photon. J. 8(4), 3900511 (2016)

    Google Scholar 

  30. S. Jiang, Y. Wang, T. Long, X. Meng, X. Yang, R. Shu, B. Sun, Information security scheme based on computational temporal ghost imaging. Sci. Rep. 7, 7676 (2017)

    Article  ADS  Google Scholar 

  31. Y. Zhang, S. Zhao, Optical encryption scheme based on ghost imaging with disordered speckles. Chinese Phys. B 26(5), 054205 (2017)

    Article  ADS  Google Scholar 

  32. S. Jiao, J. Feng, Y. Gao, T. Lei, X. Yuan, Visual cryptography in single-pixel imaging. Opt. Express 28(5), 7301–7313 (2020)

    Article  ADS  Google Scholar 

  33. P. Zheng, Q. Dai, Z. Li, Z. Ye, J. Xiong, H.C. Liu, G. Zheng, S. Zhang, Metasurface-based key for computational imaging encryption. Sci. Adv. 7(21), abg0363 (2021)

    Article  ADS  Google Scholar 

  34. Z. Zhu, H. Chi, T. Jin, S. Zheng, X. Jin, X. Zhang, Single-pixel imaging based on compressive sensing with spectral-domain optical mixing. Opt. Commun. 402, 119–122 (2017)

    Article  ADS  Google Scholar 

  35. B. Luo, P. Yin, L. Yin, G. Wu, H. Guo, Orthonormalization method in ghost imaging. Opt. Express 26(18), 29093–23106 (2018)

    Article  Google Scholar 

  36. L. Sui, J. Wang, A. Tian, A. Asundi, Optical image hiding under framework of computational ghost imaging based on an expansion strategy. Opt. Express 27(5), 7213–7225 (2019)

    Article  Google Scholar 

  37. Y. Xiao, L. Zhou, W. Chen, Experimental demonstration of ghost-imaging-based authentication in scattering media. Opt. Express 27(15), 20558–20566 (2019)

    Article  ADS  Google Scholar 

  38. J. Du, X. Xiong, C. Quan, High-efficiency optical image authentication scheme based on ghost imaging and block processing. Opt. Commun. 460, 125113 (2019)

    Article  Google Scholar 

  39. F. Wang, H. Wang, H. Wang, G. Li, G. Situ, Learning from simulation: An end-to-end deep-learning approach for computational ghost imaging. Opt. Express 27(18), 25560–25572 (2019)

    Article  ADS  Google Scholar 

  40. Y. Kang, L. Zhang, H. Ye, M. Zhao, S. Kanwal, C. Bai, D. Zhang, One-to-many optical information encryption transmission method based on temporal ghost imaging and code division multiple access. Photon. Res. 7(12), 1370–1380 (2019)

    Article  Google Scholar 

  41. L. Sui, C. Du, M. Xu, A. Tian, A. Asundi, Information encryption based on the customized data container under the framework of computational ghost imaging. Opt. Express 27(12), 16493–16506 (2019)

    Article  Google Scholar 

  42. Y. Kang, L. Zhang, H. Ye, M. Zhao, D. Zhang, Camouflaged optical encryption based on compressive ghost imaging. Opt. Lasers Eng. 134, 106154 (2020)

    Article  Google Scholar 

  43. S. Yuan, D.A. Magayane, X. Liu, X. Zhou, Z. Li, A blind watermarking scheme based on computational ghost imaging in wavelet domain. Opt. Commun. 482(1), 126568 (2021)

    Article  Google Scholar 

  44. L. Sui, C. Du, X. Zhang, A. Tian, A. Anand, Double-image encryption based on interference and logistic map under the framework of double random phase encoding. Opt. Lasers Eng. 122, 113–122 (2019)

    Article  Google Scholar 

  45. L. Sui, Z. Pang, Y. Cheng, Y. Cheng, Z. Xiao, A. Tian, K. Qian, A. Anand, An optical image encryption based on computational ghost imaging with sparse reconstruction. Opt. Lasers Eng. 143, 106627 (2021)

    Article  Google Scholar 

  46. L. Wang, S. Zhao, Fast reconstructed and high-quality ghost imaging with fast Walsh-Hadamard transform. Photon. Res. 4(6), 240–244 (2016)

    Article  Google Scholar 

  47. L. Sui, L. Zhang, Y. Cheng, Z. Xiao, A. Anand, Computational ghost imaging based on the conditional adversarial network. Opt. Commun. 492, 126982 (2021)

    Article  Google Scholar 

  48. W. Chen, Correlated-photon secured imaging by iterative phase retrieval using axially-varying distances. IEEE Photon. Technol. Lett. 28(18), 1932–1935 (2016)

    Article  ADS  Google Scholar 

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Funding

National Natural Science Foundation of China (NSFC): 62031023.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yaoling Zhou, Zhaolin Xiao & Liansheng Sui

  2. Xi’an Haitang Vocational College, Xi’an, 710038, China

    Mu Yang

  3. Yan’an Vocational and Technical College, Yan’an, 716000, China

    Bei Zhou

  4. Shaanxi Key Laboratory for Network Computing and Security Technology, Xi’an, 710048, China

    Liansheng Sui

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  1. Yaoling Zhou
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Contributions

YZ: conceptualization, methodology, software, validation, writing-original draft-preparation. MY: software, validation. BZ: software, validation. ZX: funding. LS: conceptualization, resources, supervision, writing-reviewing and editing.

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Correspondence to Liansheng Sui.

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Zhou, Y., Yang, M., Zhou, B. et al. An optical image watermarking method based on computational ghost imaging and multiple logistic maps. Appl. Phys. B 128, 134 (2022). https://doi.org/10.1007/s00340-022-07855-2

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