Skip to main content
SpringerLink
Log in

Quantum image scaling based on bilinear interpolation with arbitrary scaling ratio

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In recent years, quantum image scaling considered as one of the most common and basic operations in quantum image processing has been widely studied. In this paper, quantum algorithm based on bilinear interpolation with arbitrary scaling ratio is proposed to resize quantum images. Firstly, a quantum image with arbitrary size \( H \times W \) is described by the generalized quantum image representation. Then, bilinear interpolation is used to create new pixels (when scaling up) or delete redundant pixels (when scaling down). By utilizing the quantum operations that have been designed, the concrete circuits of quantum image scaling algorithm with arbitrary scaling ratio are implemented. Finally, the network complexity of the quantum circuits based on the basic quantum gates is analyzed and the simulation results based on the classical computer’s MATLAB software are given.

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

Similar content being viewed by others

References

  1. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  2. Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)

  3. Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

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

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

  6. 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 

  7. Le, P.Q., Dong, F.Y., 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  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum Inf. Process. 14(11), 4001–4026 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14(5), 1589–1604 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Gonzalez, R., Woods, R.: Digital Image Processing, 3rd edn. Prentice Hall, New Jersey (2007)

    Google Scholar 

  14. http://www.mathworks.cn/cn/help/images/ref/imresize.html (2014)

  15. Sang, J.Z., Wang, S., Niu, X.M.: Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR. Quantum Inf. Process. 15(1), 37–64 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Zhou, R.G., Hu, W.W., Fan, P., Ian, H.: Quantum realization of the bilinear interpolation method for NEQR. Sci. Rep. 7, 2511 (2017)

    Article  ADS  Google Scholar 

  17. Zhou, R.G., Liu, X., Luo, J.: Quantum circuit realization of the bilinear interpolation method for GQIR. Int. J. Theor. Phys. 56(9), 2966–2980 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Islam, M.S., Rahman, M.M., Begum, Z., Hafiz, M.Z.: Low cost quantum realization of reversible multiplier circuit. Inf. Technol. J. 8(2), 208–213 (2009)

    Article  Google Scholar 

  19. Thapliyal, H., Ranganathan, N.: Design of efficient reversible binary subtractors based on a new reversible gate. In: Proceedings of the IEEE Computer Society Annual Symposium on VLSI, Tampa, pp. 229–234 (2009)

  20. Thapliyal, H., Ranganathan, N.: A new design of the reversible subtractor circuit. In: 2011 11th IEEE Conference on Nanotechnology (IEEE-NANO), IEEE, pp. 1430–1435 (2011)

  21. Kotiyal, S., Thapliyal, H., Ranganathan, N.: Circuit for reversible quantum multiplier based on binary tree optimizing Ancilla and garbage bits. In: 2014 27th International Conference on VLSI Design and 2014 13th International Conference on Embedded Systems, IEEE, pp. 545–550 (2014)

  22. Khosropour, A., Aghababa, H., Forouzandeh, B.: Quantum division circuit based on restoring division algorithm. In: Eighth International Conference on Information Technology: New Generations, Itng 2011, Las Vegas, 11–13 April, DBLP, pp. 1037–1040, (2011)

  23. Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the National Key R&D Plan under Grant Nos. 2018YFC1200200 and 2018YFC1200205, National Natural Science Foundation of China under Grant No. 61463016 and “Science and Technology Innovation Action Plan” of Shanghai in 2017 under Grant No. 17510740300.

Author information

Authors and Affiliations

  1. College of Information Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Ri-Gui Zhou, Yu Cheng & DaQian Liu

  2. Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai, 201306, China

    Ri-Gui Zhou, Yu Cheng & DaQian Liu

Authors
  1. Ri-Gui Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. DaQian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Cheng.

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

Zhou, RG., Cheng, Y. & Liu, D. Quantum image scaling based on bilinear interpolation with arbitrary scaling ratio. Quantum Inf Process 18, 267 (2019). https://doi.org/10.1007/s11128-019-2377-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2377-4

Keywords

Search

Navigation