Skip to main content

Quantum Image Representations

  • Chapter
  • First Online:
Book cover Quantum Image Processing

Abstract

In this chapter, mainstream QIRs are reviewed and classified into three models based on different requirements to capture the content of an image. They are thoroughly compared in terms of their color information encoding strategies, computational complexities of preparation, and measurement-based retrievals. The preparation, compression, and retrieval of FRQI, MCQI, and NEQR representations are fully introduced. While designing the position and color transformations of these QIRs, some definitions and theorems are given, which will guide in part the subsequent QIMP studies.

Ⓒ Portions of this chapter are reprinted from ref. [28], with permission of Springer.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

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

    Google Scholar 

  2. Caraiman, S., Manta, V.: Image segmentation on a quantum computer. Quantum Inf. Process. 14(5), 1693–1715 (2015)

    Article  MathSciNet  Google Scholar 

  3. Fan, P., Zhou, R., Jing, N., Li, H.: Geometric transformations of multidimensional color images based on NASS. Inf. Sci. 340–341, 191–208 (2016)

    Article  Google Scholar 

  4. Hillman, P., Hannah, J., Renshaw, D.: Alpha channel estimation in high resolution images and image sequences. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1063–1068 (2001)

    Google Scholar 

  5. Iliyasu, A.: Algorithmic frameworks to support the realisation of secure and efficient image-video processing applications on quantum computers. Ph.D Thesis, Tokyo Institute of Technology, Tokyo (2012)

    Google Scholar 

  6. Iliyasu, A., Le, P., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)

    Article  MathSciNet  Google Scholar 

  7. Iliyasu, A., Le, P., Fangyan, D., Hirota, K.: Restricted geometric transformations and their applications for quantum image watermarking and authentication. In: Proceeding of the 10th Asian Conference on Quantum Information Sciences (AQIS 2010), pp. 96–97 (2010)

    Google Scholar 

  8. Jiang, N., Lu, X., Hu, H., Dang, Y., Cai, Y.: A novel quantum image compression method based on JPEG. Int. J. Theor. Phys. 57(3), 611–636 (2018)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  10. Le, P., 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)

    Google Scholar 

  11. Le, P., Iliyasu, A., Dong, F., Hirota, K.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40(3), 113–123 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Le, P., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10(1), 63–84 (2011)

    Article  MathSciNet  Google Scholar 

  13. Le, P., Iliyasu, A., Dong, F., Hirota, K.: Efficient colour transformations on quantum image. J. Adv. Comput. Intell. Intell. Inf. 15(6), 698–706 (2011)

    Article  Google Scholar 

  14. Le, P., Iliyasu, A., Dong, F., Hirota, K.: A flexible representation and invertible transformations for images on quantum computers. New Adv. Intell. Signal Process. Stud. Comput. Intell. 372, 179–202 (2011)

    Article  Google Scholar 

  15. Le, P., Iliyasu, A., Dong, F., Hirota, K.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412(15), 1406–1418 (2011)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Li, H., Fan, P., Xia, H., Song, S., He, X.: The multi-level and multi-dimensional quantum wavelet packet transforms. Sci. Rep. 8, 13884 (2018)

    Article  Google Scholar 

  19. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  20. Pang, C., Zhou, Z., Guo, G.: A hybrid quantum encoding algorithm of vector quantization for image compression. arXiv:cs/0605002v3[cs.MM] (2006)

    Google Scholar 

  21. Plataniotis, K., Venetsanopoulos, A.: Color Image Processing and Applications. Springer, Berlin (2000)

    Book  Google Scholar 

  22. Song, X., Wang, S., Niu, X.: Multi-channel quantum image representation based on phase transform and elementary transformations. J. Inf. Hiding Multimedia Signal Process. 5(4), 574–585 (2014)

    Google Scholar 

  23. Sun, B., Le, P., Iliyasu, A., Yan, F., Garcia, J., Dong, F., Hirota, K.: A multi-channel representation for images on quantum computers using the RGBα color space. In: IEEE 7th International Symposium on Intelligent Signal Processing (WISP), pp. 1–6 (2011)

    Google Scholar 

  24. 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. Inf. 17(3), 404–417 (2013)

    Article  Google Scholar 

  25. Sun, B., Iliyasu, A., Yan, F., Garcia, J., Dong, F., Al-Asmari, A., Hirota, K.: Multi-channel information operations on quantum images. J. Adv. Comput. Intell. Intell. Inf. 18(2), 140–149 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  27. Venegas-Andraca, S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation, vol. 5105, pp. 137–147 (2003)

    Google Scholar 

  28. Yan, F., Iliyasu, A., Venegas-Andraca, S.: A survey of quantum image representations. Quantum Inf. Process. 15(1), 1–35 (2016)

    Article  MathSciNet  Google Scholar 

  29. Yang, Y., Jia, X., Sun, S., Pan, Q.: Quantum cryptographic algorithm for color images using quantum Fourier transform and double random-phase encoding. Inf. Sci. 277, 445–457 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Yan, F., Venegas-Andraca, S.E. (2020). Quantum Image Representations. In: Quantum Image Processing. Springer, Singapore. https://doi.org/10.1007/978-981-32-9331-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-32-9331-1_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-32-9330-4

  • Online ISBN: 978-981-32-9331-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics