Improved Quantum Image Median Filtering in the Spatial Domain

  • SheXiang Jiang
  • Ri-Gui ZhouEmail author
  • WenWen Hu
  • YaoChong Li


In some image processing algorithms, such as those for image feature extraction and segmentation, filtering is a significant pre-processing step to remove noises and improve image quality. An improved quantum image median filtering approach is proposed, and its corresponding quantum circuit is designed in this work. The main idea of the approach is that first the classical image is converted into a quantum version based on the novel enhanced quantum representation (NEQR) of digital images, and then a unique quantum module is designed to realize the median calculation of neighborhood pixels for each pixel point in the image. Finally, in order to improve the filtering effect, extremum detection is employed to distinguish noises from true signals. The experimental results show that a competitive filtering performance is obtained compared with previous methods. In addition, a network complexity analysis of the quantum circuit suggests that the proposed filtering approach can perform enormous speed-up over its corresponding classical counterparts.


Quantum image processing Quantum image filtering Median filtering Extremum detection 



This work is supported by National Key R&D Plan under Grant No. 2018YFC1200200; the National Natural Science Foundation of China under Grant No.61463016 and No.61763014; Science and technology innovation action plan of Shanghai in 2017 under Grant No.17510740300.


  1. 1.
    Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Nagy, M., Akl, S.G.: Quantum computation and quantum information. Int. J. Parallel, Emergent Distrib.Syst. 21, 1–59 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Kanamori, Y., Yoo, S.M., Pan, W.D., Sheldon, F.T.: A short survey on quantum computers. Int. J. Comput. Appl. 28, 227–233 (2006)Google Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Venegas-Andraca, S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation. 5105(8), 134–147(2003)Google Scholar
  7. 7.
    Venegas-Andraca, S., Ball, J.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Latorre, J.: Image Compression and Entanglement. arXiv:quant-ph/0510031 (2005)Google Scholar
  9. 9.
    Le, P., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10, 63–84 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Zhang, Y., Lu, K., Gao, Y., Mao, W.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12, 2833–2860 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12, 3103–3126 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14, 1559–1571 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Zhou, R., Hu, W., Liu, X., Fan, P., Luo, G.: Quantum realization of the nearest neighbor value interpolation method for INEQR. Quantum Inf. Process. 17, 1–37 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Zhou, R.G., Hu, W.W., Fan, P., Ian, H.: Quantum realization of the bilinear interpolation method for NEQR. Sci. Rep. 7(2511), (2017)Google Scholar
  15. 15.
    Zhang, Y., Lu, K., Xu, K., Gao, Y., Wilson, R.: Local feature point extraction for quantum images. Quantum Inf. Process. 14, 1573–1588 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Zhang, Y., Lu, K., et al.: QSobel: a novel quantum image edge extraction algorithm. Sci. China Inf. Scis. 58, 1–13 (2015)zbMATHGoogle Scholar
  17. 17.
    Zhou, R.G., Tan, C.Y., Ian, H.: Global and local translation designs of quantum image based on FRQI. Int. J. Theor. Phys. 56, 1382–1398 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Le, P.Q., Iliyasu, A.M., Dong, F., et al.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412, 1406–1418 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Le, P.Q., Iliyasu, A.M., Dong, F., et al.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40, (2010)Google Scholar
  20. 20.
    Luo, G.F., Zhou, R.G., Liu, X.A., Hu, W.W., Luo, J.: Fuzzy matching based on gray-scale difference for quantum images. Int. J. Theor. Phys. 57, 2447–2460 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Jiang, N., Dang, Y.J., Wang, J.: Quantum image matching. Quantum Inf. Process. 15, 3543–3572 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Dang, Y., Jiang, N., Zhang, W., Hu, H.: analysis and improvement of the quantum image matching. Quantum Inf. Process. 16, 1–13 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Li, H.S., Zhu, Q.X., Lan, S., et al.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12, 2269–2290 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Caraiman, S., Manta, V.I.: Image segmentation on a quantum computer. Quantum Inf. Process. 14, 1693–1715 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Zhou, R.G., Hu, W.W., Fan, P., Luo, G.F.: Quantum color image watermarking based on Arnold transformation and LSB steganography. Int. J. Quantum. Inf. 16, 1850021 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Zhou, R.G., Hu, W.W., Fan, P.: Quantum watermarking scheme through Arnold scrambling and LSB steganography. Quantum Inf. Process. 16(212), (2017)Google Scholar
  27. 27.
    Yang, Y.G., Wang, Y., Zhao, Q.Q.: Letter to the editor regarding “dynamic watermarking scheme for quantum images based on Hadamard transform” by song et al. Multimedia Syst. 22, 271–272 (2016)CrossRefGoogle Scholar
  28. 28.
    Yang, Y.G., Jia, X., Xu, P., Tian, J.: Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12, 2765–2769 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Heidari, S., Naseri, M.: A novel LSB based quantum image watermarking. Int. J. Theor. Phys. 55, 4205–4218 (2016)CrossRefzbMATHGoogle Scholar
  30. 30.
    Heidari, S., Farzadnia, E.: A novel quantum LSB-based steganography method using the gray code for colored quantum images. Quantum Inf. Process. 16, 1–28 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moir pattern. Int. J. Theor. Phys. 54, 1021–1032 (2015)CrossRefzbMATHGoogle Scholar
  32. 32.
    Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55, 107–123 (2016)CrossRefzbMATHGoogle Scholar
  33. 33.
    Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible arXiv:quant-ph/0309070 (2003)Google Scholar
  34. 34.
    Caraiman, S., Manta, V.I.: Quantum image filtering in the frequency domain. Adv. Electr. Comput. Eng. 13, 77–84 (2013)CrossRefGoogle Scholar
  35. 35.
    Yuan, S., Lu, Y., Mao, X., Luo, Y., Yuan, J.: Improved quantum image filtering in the spatial domain. Int. J. Theor. Phys. 57, 804–813 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Li, P., Liu, X., Xiao, H.: Quantum image weighted average filtering in spatial domain. Int. J. Theor. Phys. 56, 3690–3716 (2017)CrossRefzbMATHGoogle Scholar
  37. 37.
    Li, P., Liu, X., Xiao, H.: Quantum image median filtering in the spatial domain. Quantum Inf. Process. 17(49), (2018)Google Scholar
  38. 38.
    Li, P., Xiao, H.: An improved filtering method for quantum color image in frequency domain. Int. J. Theor. Phys. 57, 258–278 (2018)CrossRefzbMATHGoogle Scholar
  39. 39.
    Han, T.: Research of fast median filtering algorithm and hardware implementation based on FPGA. Chinese Journal of Electron Devices. 40, 697–701 (2017)Google Scholar
  40. 40.
    Wang, D., University, H: Kaifeng: Design of Quantum Comparator Based on extended general Toffoli gates with multiple targets. Comput. Sci. 39, 302–306 (2012)Google Scholar
  41. 41.
    Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process Mathematic, 1589–1604 (2015), 14Google Scholar

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Authors and Affiliations

  1. 1.College of Information EngineeringShanghai Maritime UniversityShanghaiChina
  2. 2.Research Center of Intelligent Information Processing and Quantum Intelligent ComputingShanghaiChina
  3. 3.School of Computer Science and EngineeringAnhui University of Science and TechnologyHuainanChina

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