Skip to main content
SpringerLink
Log in

Quantum Representation of Indexed Images and its Applications

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Indexed images have been widely used in classical digital image processing, however there have been no reports on the representation and applications of indexed images in quantum image processing so far. To solve the representation problem of indexed images on a quantum computer, a quantum indexed image representation (QIIR) method is proposed in the paper. A quantum indexed image consists of a quantum data matrix and a quantum palette matrix. Each data structure is based on the basic states of qubit sequence to represent information, including pixel positions and pixel values in the data matrix, and indexes and color values in the palette matrix. Several simple geometric and color transformations of quantum indexed images are presented later, including orthogonal rotation, cyclic shift, color inversion, color replacement and color look-up. Finally, a quantum indexed image steganography based on EzStego is proposed. In this scheme, the distance between two arbitrary color values in the quantum palette is first calculated, and then several effective color pairs are obtained. At last, according to embedded message bits, pixel values in the data matrix are updated in light of effective color pairs, and a new quantum data matrix with embedded message is obtained. The proposed scheme can be executed on a future quantum computer. The feasibility and validness of this scheme are verified on a classical computer from four aspects: visual quality, embedding capacity, robustness and security.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

References

  1. Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proc. SPIE Conf. Quantum Inf. Comput. 5105, 137–147 (2003)

    ADS  Google Scholar 

  2. Latorre, J.I.: Image compression and entanglement. arXiv:quant-ph/0510031 (2005)

  3. Le, P.Q., Dong, F., Hirota, K.: Flexible representation of quantum images and its computational complexity analysis. In: Proceedings of the 10th Symposium on Advanced Intelligent Systems (ISIS 2009), pp. 146–149 (2009)

  4. Sun, B., Iliyasu, A., Yan, F., Dong, F., Hirota, K.: An RGB multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Info. 17(3), 404–417 (2013)

    Article  Google Scholar 

  5. Caraiman, S., Manta, V.: Image processing using quantum computing. In: IEEE 16th International Conference on System Theory, Control and Computing (ICSTCC), pp. 1–6 (2012)

  6. Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  7. Zhang, Y., Lu, K., Gao, Y.H., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3103–3126 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  8. Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., Compare, A.: SQR: a simple quantum representation of infrared images. Quantum Inf. Process. 13 (6), 1353–1379 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  9. Li, H.S., Zhu, Q.X., Song, L., Shen, C.Y., Zhou, R.G., Mo, J.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12(6), 2269–2290 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  10. Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)

    Article  MathSciNet  Google Scholar 

  11. Li, H.S., Zhu, Q.X., Zhou, R.G., Song, L., Yang, X.J.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Inf. Process. 13(4), 991–1011 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  12. Sahin, E., Yilmaz, I.: QRMW: quantum representation of multi wavelength images. Turk. J. of Elec. Eng. Comp. Sci. 26(2), 768–779 (2018)

    Article  Google Scholar 

  13. Li, P.C., Liu, X.D.: Color image representation model and its application based on an improved FRQI. Int. J. Quantum Inf. 16(1), 185000 (2018)

    Article  Google Scholar 

  14. Liu, K., Zhang, Y.Z., Lu, K., Wang, X.P., Wang, X.: An optimized quantum representation for color digital images. Int. J. Theor. Phys. 57(10), 2938–2948 (2018)

    Article  Google Scholar 

  15. Jang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55(1), 107–123 (2016)

    Article  Google Scholar 

  16. Zhou, R.G., Luo, J., Liu, X.A., Zhu, C., Wei, L., Zhang, X.: A novel quantum image steganography scheme based on LSB. Int. J. Theor. Phys. 57(6), 1848–1863 (2018)

    Article  MathSciNet  Google Scholar 

  17. Heidari, S., Farzadnia, E.: A novel quantum LSB-based steganography method using the gray code for colored quantum images. Quantum Inf. Process. 16(10), 242 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  18. Li, P.C., Lu, A.P.: LSB-based steganography using reflected gray code for color quantum images. Int. J. Theor. Phys. 57(5), 1516–1548 (2018)

    Article  MathSciNet  Google Scholar 

  19. Sahin, E., Yilmaz, I.: A novel quantum steganography algorithm based on LSBq for multi-wavelength quantum images. Quantum Inf. Process. 17, 319 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  20. Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)

    Article  Google Scholar 

  21. Wang, D., Liu, Z.H., Zhu, W.N., Li, S.Z.: Design of quantum comparator based on extended general toffoli gates with multiple targets. Computer Science 39(9), 302–306 (2012)

    Google Scholar 

  22. Jiang, N.: Quantum Image Processing, pp 21–22. Tsinghua University Press, Beijing (2016)

    Google Scholar 

  23. Zhang, Y., Lu, K., Xu, K., Gao, Y.H.: Local feature point extraction for quantum images. Quantum Inf. Process. 14(5), 1573–1588 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. Vlatko, V., Adriano, B., Artur, E.: Quantum networks for elementary arithmetic operations. Phys. Rev. A. 54(1), 147–153 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  25. Tang, S.F.: The Principle of Computer Composition, 2nd edn., pp 222–237. Higher Education Process, Beijing (2008)

    Google Scholar 

  26. Al-Salhi, Y.E.A., Lu, S.: Quantum image steganography and steganalysis based on LSQu-blocks image information concealing algorithm. Int. J. Theor. Phys. 55(8), 3722–3736 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors appreciate the kind comments and constructive suggestions of the anonymous reviewers. This work is supported by the Youth Science Foundation of Northeast Petroleum University (Grant No. 2018QNL-08), the Excellent Young and Middle-aged Scientific Research Innovation Team of Northeast Petroleum University (Grant No. KYCXTD201903), the Natural Science Foundation of Heilongjiang Province of China (Grant No. F2016002), PetroChina Innovation Foundation (Grant No. 2018D-5007-0302) and the Postdoctoral Foundation of Heilongjiang Province of China (Grant No. LBH-Z18045).

Author information

Authors and Affiliations

  1. School of Computer & Information Technology, Northeast Petroleum University, Daqing, 163318, China

    Bing Wang, Meng-qi Hao, Pan-chi Li & Zong-bao Liu

Authors
  1. Bing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng-qi Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pan-chi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zong-bao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bing Wang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, B., Hao, Mq., Li, Pc. et al. Quantum Representation of Indexed Images and its Applications. Int J Theor Phys 59, 374–402 (2020). https://doi.org/10.1007/s10773-019-04331-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-019-04331-0

Keywords

Search

Navigation