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Quantum image mid-point filter

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Abstract

Mid-point filter is an order statistic filter which cannot be realized in the frequency domain. It is used for de-noising Gaussian noise effectively. In this paper, a new method for quantum realization mid-point filter in the spatial domain is proposed. An enhanced method for preparing multiple copies of the same image is also proposed. The modular design of the quantum circuit was utilized with an articulation on reducing the number of ancillary qubits. In this work, we present the quantum circuit for the three basic modules (cyclic shift, swap and division by two) and four composite modules (full adder, comparator, sort and maximum–minimum extraction). Also, the enhanced quantum preparation of multiple copies of an image is introduced. Moreover, the design of maximum–minimum extraction is modified to adapt our quantum circuit design. Finally, the complete quantum circuit which implements the mid-point filtering task is constructed and the results of several simulation experiments with different noise patterns are presented on some grayscale images. Apparently, the proposed approach has identical noise suppression of the classical version; however, there is a clear reduction in the complexity from exponential function of image size \(O(2^{2n})\) to the second-order polynomial \(O(n^{2} + q)\).

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References

  1. Caraiman, S., Manta, V.I.: Quantum image filtering in the frequency domain. Adv. Electr. Comput. Eng. 13(3), 77–84 (2013). https://doi.org/10.4316/AECE.2013.03013

    Article  Google Scholar 

  2. Caraiman, S., Manta, V.I.: Image segmentation on a quantum computer. Quantum Inf. Process. 14(5), 1693–1715 (2015). https://doi.org/10.1007/s11128-015-0932-1

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Cuccaro, S.A., Draper, T.G., Kutin, S.A., Moulton, D.P.: A new quantum ripple-carry addition circuit. arXiv preprint arXiv:quant-ph/0410184 (2004)

  4. Du, S., Qiu, D., Mateus, P., Gruska, J.: Enhanced double random phase encryption of quantum images. Results Phys. 13, 102161 (2019). https://doi.org/10.1016/j.rinp.2019.102161

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice-Hall, Upper Saddle River (2006)

    Google Scholar 

  7. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, ACM, New York, NY, USA, STOC’96, pp. 212–219 (1996). https://doi.org/10.1145/237814.237866

  8. Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2015). https://doi.org/10.1007/s11128-014-0841-8

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. 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). https://doi.org/10.1007/s11128-015-1099-5

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Jiang, N., Zhao, N., Wang, L.: Lsb based quantum image steganography algorithm. Int. J. Theor. Phys. 55(1), 107–123 (2016). https://doi.org/10.1007/s10773-015-2640-0

    Article  MATH  Google Scholar 

  11. Jiang, S., Zhou, R.G., Hu, W., Li, Y.: Improved quantum image median filtering in the spatial domain. Int. J. Theor. Phys. 58(7), 2115–2133 (2019). https://doi.org/10.1007/s10773-019-04103-w

    Article  MathSciNet  MATH  Google Scholar 

  12. Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Fast geometric transformations on quantum images. Int. J. Appl. Math. 40, 3 (2010)

    MathSciNet  MATH  Google Scholar 

  13. Le, P.Q., 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 (2011a). https://doi.org/10.1007/s11128-010-0177-y

    Article  MathSciNet  MATH  Google Scholar 

  14. Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412(15), 1406–1418 (2011). https://doi.org/10.1016/j.tcs.2010.11.029

    Article  MathSciNet  MATH  Google Scholar 

  15. Li, H.S., Qingxin, Z., Lan, S., Shen, C.Y., Zhou, R., Mo, J.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12(6), 2269–2290 (2013). https://doi.org/10.1007/s11128-012-0521-5

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Li, P., Liu, X., Xiao, H.: Quantum image weighted average filtering in spatial domain. Int. J. Theor. Phys. 56(11), 3690–3716 (2017). https://doi.org/10.1007/s10773-017-3533-1

    Article  MATH  Google Scholar 

  17. Li, P., Liu, X., Xiao, H.: Quantum image median filtering in the spatial domain. Quantum Inf. Process. 17(3), 49 (2018). https://doi.org/10.1007/s11128-018-1826-9

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible. arXiv preprint arXiv:quant-ph/0309070 (2003)

  19. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th edn. Cambridge University Press, New York (2011)

    MATH  Google Scholar 

  20. Sang, J., Wang, S., Niu, X.: Quantum realization of the nearest-neighbor interpolation method for frqi and neqr. Quantum Inf. Process. 15(1), 37–64 (2016). https://doi.org/10.1007/s11128-015-1135-5

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994). https://doi.org/10.1109/SFCS.1994.365700

  22. Venegas-Andraca, S.E., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Donkor, E., Pirich, A.R., Brandt, H.E. (eds.) Quantum Information and Computation, International Society for Optics and Photonics, SPIE, vol. 5105, pp. 137–147 (2003). https://doi.org/10.1117/12.485960

  23. Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14(5), 1589–1604 (2015). https://doi.org/10.1007/s11128-014-0843-6

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Xia, H., Li, H., Zhang, H., Liang, Y., Xin, J.: An efficient design of reversible multi-bit quantum comparator via only a single ancillary bit. Int. J. Theor. Phys. 57(12), 3727–3744 (2018). https://doi.org/10.1007/s10773-018-3886-0

    Article  MATH  Google Scholar 

  25. Yan, F., Iliyasu, A.M., Jiang, Z.: Quantum computation-based image representation, processing operations and their applications. Entropy 16(10), 5290–5338 (2014). https://doi.org/10.3390/e16105290

    Article  ADS  MathSciNet  Google Scholar 

  26. Yan, F., Iliyasu, A.M., Venegas-Andraca, S.E.: A survey of quantum image representations. Quantum Inf. Process. 15(1), 1–35 (2016). https://doi.org/10.1007/s11128-015-1195-6

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Yuan, S., Mao, X., Zhou, J., Wang, X.: Quantum image filtering in the spatial domain. Int. J. Theor. Phys. 56(8), 2495–2511 (2017). https://doi.org/10.1007/s10773-017-3403-x

    Article  MATH  Google Scholar 

  28. Yuan, S., Lu, Y., Mao, X., Luo, Y., Yuan, J.: Improved quantum image filtering in the spatial domain. Int. J. Theor. Phys. 57(3), 804–813 (2018). https://doi.org/10.1007/s10773-017-3614-1

    Article  MathSciNet  MATH  Google Scholar 

  29. 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). https://doi.org/10.1007/s11128-013-0567-z

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Zhang, Y., Lu, K., Xu, K., Gao, Y., Wilson, R.: Local feature point extraction for quantum images. Quantum Inf. Process. 14(5), 1573–1588 (2015). https://doi.org/10.1007/s11128-014-0842-7

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Zhou, R., Hu, W., Luo, G., Liu, X., Fan, P.: Quantum realization of the nearest neighbor value interpolation method for ineqr. Quantum Inf. Process. 17(7), 166 (2018). https://doi.org/10.1007/s11128-018-1921-y

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Zhou, R.G., Hu, W., Fan, P., Ian, H.: Quantum realization of the bilinear interpolation method for neqr. Sci.c Rep. 7(1), 2511 (2017a). https://doi.org/10.1038/s41598-017-02575-6

    Article  ADS  Google Scholar 

  33. Zhou, R.G., Tan, C., Ian, H.: Global and local translation designs of quantum image based on frqi. Int. J. Theor. Phys. 56(4), 1382–1398 (2017b). https://doi.org/10.1007/s10773-017-3279-9

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, Faculty of Computers and Artificial Intelligence, Helwan University, Cairo, Egypt

    Abdalla Essam Ali, Hala Abdel-Galil & Soha Mohamed

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  1. Abdalla Essam Ali
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  2. Hala Abdel-Galil
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  3. Soha Mohamed
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Correspondence to Abdalla Essam Ali.

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Ali, A.E., Abdel-Galil, H. & Mohamed, S. Quantum image mid-point filter. Quantum Inf Process 19, 238 (2020). https://doi.org/10.1007/s11128-020-02738-x

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