Realization of quantum mean filters with different sized on NEQR quantum images by QFT based operations

Year 2023, Volume: 12 Issue: 1, 1 - 12, 10.03.2023

Engin Şahin

https://doi.org/10.55859/ijiss.1210521

Abstract

For some image processing algorithms such as edge detection and segmentation, filtering in the spatial domain is an important pre-processing to improve the quality of the image by removing the noise in the images. The time and memory requirements for processing also increase as the size of the images increases. Besides, excessive blurring of the image during noise removal operation can lead to excessive deterioration of image quality. Therefore, the balance between noise reduction and blur needs to be well adjusted. In this paper, a new quantum method for noise reduction on quantum images using QFT-based arithmetic operators is proposed and quantum circuits are designed. Mean filtering operators of different sizes are used to remove noise. First, the classical image is represented by the gray scale quantum image model, the novel enhanced quantum representation (NEQR) model. A quantum method is proposed and circuits are presented for the realization of Mean filters of different sizes on the basis of addition and division operations. Finally, the performance of the method is evaluated by presenting the circuit complexity of the method and the experimental results. In the proposed method, it is aimed to use less resources and reduce the circuit complexity. The optimal filtering operator size is investigated for the balance between noise reduction and image blur.

Keywords

quantum computing, quantum image processing, noise reduction, image smoothing, mean filter

References

• Referans1 T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J.L. OBrien, \emph{Quantum computers}, Nature, vol. 464, no. 7285, pp. 45, 2010.
• Referans2 M. Mandviwalla, K. Ohshiro and B. Ji, \emph{Implementing Grover’s algorithm on the IBM quantum computers}, In Proceedings of the 2018 IEEE International Conference on Big Data, Seattle, WA, USA, pp. 2531–2537, 2018.
• Referans3 E. \c{S}ahin, \emph{Implementation of addition and subtraction based on quantum Fourier transform on IBM quantum computer}, In Proceedings of the 2nd International Symposium of Scientific Research and Innovative Studies, Bandirma, Balikesir, Turkey, pp. 593–605, 2022.
• Referans4 M. A. Nielsen, and I. L. Chuang, \emph{Quantum Computation and Quantum Information: 10th Anniversary Edition}. Cambridge University Press, New York, NY, USA, 2011.
• Referans5 E. \c{S}ahin, and I. Yilmaz, \emph{A quantum edge detection algorithm for quantum multi-wavelength images}, Int. J. Quantum Inform., vol. 19, no. 3, 2150017, 2021.
• Referans6 P. Q. Le, F. Dong, and K. Hirota, \emph{A flexible representation of quantum images for polynomial preparation, image compression, and processing operations}, Quantum Inf. Process., vol. 10, pp. 63–84, 2011.
• Referans7 B. Sun, A. Iliyasu, F. Yan, F. Dong, and K. Hirota, \emph{An RGB multi-channel representation for images on quantum computers}, J. of Adv. Comp. Intelligence and Intelligent Informatics, vol. 17, no. 3, pp. 404–417, 2013.
• Referans8 Y. Zhang, K. Lu, Y. Gao, and M. Wang, \emph{A novel enhanced quantum representation of digital images}, Quantum Inf. Process., vol. 12, no. 8, pp. 2833–2860, 2013.
• Referans9 J. Z. Sang, S. Wang, and Q. Li, Q. \emph{A novel quantum representation of color digital images}, Quantum Inf. Process., vol. 16, pp. 14, 2017.
• Referans10 E. \c{S}ahin, and \.{I}. Yilmaz, \emph{QRMW: quantum representation of multi wavelength images}, Turk. J. Electr. Eng. Comput. Sci., vol. 26, no. 2, pp. 768–779, 2018.
• Referans11 J. Su, X. Guo, C. Liu and L. Li, \emph{A new trend of quantum image representations}, IEEE Access, vol. 8, pp. 214520–214537, 2020.
• Referans12 S. Jiang, R. G. Zhou, W. Hu, and Y. Li, \emph{Improved quantum image median filtering in the spatial domain}, Int. J. Theor. Phys., vol. 58, pp. 2115–2133, 2019.
• Referans13 C. Lomont, \emph{Quantum convolution and quantum correlation algorithms are physically impossible}, arXiv preprint arXiv:quant-ph/0309070, 2003.
• Referans14 S. Yuan, X. Mao, J. Zhou, and X. Wang, \emph{Quantum image filtering in the spatial domain}, Int. J. Theor. Phys., vol. 56, no. 8, pp. 2495–2511, 2017.
• Referans15 S. Yuan, Y. Lu, X. Mao, Y. Luo, and J. Yuan, \emph{Improved quantum image filtering in the spatial domain}, Int. J. Theor. Phys., vol. 57, no. 3, pp. 804–813, 2018.
• Referans16 P. Li, X. Liu, and H. Xiao, \emph{Quantum image weighted average filtering in spatial domain}, Int. J. Theor. Phys., vol. 56, no.11, pp. 3690–3716, 2017.
• Referans17 P. Li, X. Liu, and H. Xiao, \emph{Quantum image median filtering in the spatial domain}, Quantum Inf. Process., vol. 17, no. 3, pp. 49, 2018.
• Referans18 A. E. Ali, H. Abdel-Galil, and S. Mohamed, \emph{Quantum image mid-point filter}, Quantum Inf. Process., vol. 19, pp. 238, 2020.
• Referans19 E. \c{S}ahin, \emph{Quantum arithmetic operations based on quantum Fourier transform on signed integers}, Int. J. Quantum Inform., vol. 18, no. 6, 2050035, 2020.
• Referans20 P. Q. Le, A. M. Iliyasu, F. Dong and K. Hirota, \emph{Strategies for designing geometric transformations on quantum images}, Theor. Comput. Sci., vol. 412, no. 15, pp. 1406--1418, 2011.