2D-filter design based on Volterra equation and machine learning ‎to tackle the aliasing effect in image demosicing

  • Authors

    • Nodjigoto Blague PhD Student
    • Boukar Ousman Professor
    • Libouga Li Gwet David Ph.D
    • Kamgang Jean Claude Professor
    • Ndogotar Nelio Ph.D

    Received date: January 23, 2025

    Accepted date: March 19, 2025

    Published date: March 20, 2025

    https://doi.org/10.14419/50xc1e97
  • 2-Dimensional Discrete Volterra Equation; Perceptron; Aliasing; Demosaicing.

  • Abstract

    For nonlinear problems, the discrete Volterra equation is a helpful model. An aliasing effect between components from a CFA image is ‎known as the main problem in Demosaicing on frequency-domain analysis, which denotes a nonlinear problem. The discrete Volterra equa-‎tion can be used as a model to solve Demosaicing. A suitable Volterra kernel is required. We show that there is an analogy between the ‎weights and bias of the perceptron and the coefficients of the Volterra kernel. This analogy allows us to discover the coefficients of 2D-‎nonlinear filters by numerically solving the discrete Volterra equation. On the images from the Kodak database, this Demosaicing procedure ‎is applied in accordance with the Volterra equation's order and the Volterra kernel's size. Effectiveness is judged using several measures. ‎The study's findings show that the aliasing effect is lessened depending on the order of the Volterra equation and the Volterra kernel size ‎chosen. Our mean signal-to-noise ratio performance, using a 3x3 kernel size and the second-order Volterra equation, is 37.7 dB.

  • References

    1. Alleysson, David, Sabine Susstrunk, and Jeanny Hérault. "Linear demosaicing inspired by the human visual system." IEEE Transac-tions on Image Processing 14, no. 4 (2005): 439-449. https://doi.org/10.1109/TIP.2004.841200.
    2. Dubois, Eric. "Frequency-domain methods for demosaicking of Bayer-sampled color images." IEEE Signal Processing Letters 12, no. 12 (2005): 847-850. https://doi.org/10.1109/LSP.2005.859503.
    3. McCulloch, Warren S., and Walter Pitts. "A logical calculus of the ideas immanent in nervous activity." The bulletin of mathematical biophysics 5 (1943): 115-133. https://doi.org/10.1007/BF02478259
    4. Amari, Shun-ichi. "Backpropagation and stochastic gradient descent method." Neurocomputing 5, no. 4-5 (1993): 185-196. https://doi.org/10.1016/0925-2312(93)90006-O
    5. Marmarelis, Vasilis Z., and Xiao Zhao. "Volterra models and three-layer perceptrons." IEEE Transactions on neural networks 8, no. 6 (1997): 1421-1433. https://doi.org/10.1109/72.641465.
    6. Kiku, Daisuke, Yusuke Monno, Masayuki Tanaka, and Masatoshi Okutomi. "Beyond color difference: Residual interpolation for color image demosaicking." IEEE Transactions on Image Processing 25, no. 3 (2016): 1288-1300. https://doi.org/10.1109/TIP.2016.2518082.
    7. Oh, Paul, Sukho Lee, and Moon Gi Kang. "Colorization-based RGB-white color interpolation using color filter array with randomly sampled pattern." Sensors 17, no. 7 (2017): 1523. https://doi.org/10.3390/s17071523.
    8. B. E. Bayer, “colour imaging array,” U.S. Patent 3 971 065, July 1976.
    9. Kodak Lossless True Colour Image Suite, (Online). Available from: http://r0k.us/graphics/kodak/〉 (accessed 01.07.2024).
    10. Libouga, Ideal Oscar, Laurent Bitjoka, David Libouga Li Gwet, Ousman Boukar, and Alexandre Michel Njan Nlôga. "A supervised U-Net based color image semantic segmentation for detection & classification of human intestinal parasites." e-Prime-Advances in Elec-trical Engineering, Electronics and Energy 2 (2022): 100069. https://doi.org/10.1016/j.prime.2022.100069.
    11. Elsayed, Mahmoud, Fawaz Sammani, Abdelsalam Hamdi, Asem Albaser, and Haitham Babalghoom. "A new method for full reference image blur measure." Int J Simul Syst Sci Technol 19, no. 4 (2018). https://doi.org/10.5013/IJSSST.a.19.01.7.
    12. Yang, Yanqin, Olivier Losson, and Luc Duvieubourg. "Quality evaluation of color demosaicing according to image resolution." In 2007 Third International IEEE Conference on Signal-Image Technologies and Internet-Based System, pp. 689-695. IEEE, 2007. https://doi.org/10.1109/SITIS.2007.33.
    13. Lu, Wenmiao, and Yap-Peng Tan. "Color filter array demosaicking: new method and performance measures." IEEE transactions on image processing 12, no. 10 (2003): 1194-1210. https://doi.org/10.1109/TIP.2003.816004
    14. Kim, Hansol, Sukho Lee, and Moon Gi Kang. "Demosaicing of RGBW color filter array based on rank minimization with colorization constraint." Sensors 20, no. 16 (2020): 4458. https://doi.org/10.3390/s20164458
    15. Jeong, Kyeonghoon, Jonghyun Kim, and Moon Gi Kang. "Color demosaicing of RGBW color filter array based on laplacian pyramid." Sensors 22, no. 8 (2022): 2981. https://doi.org/10.3390/s22082981.

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  • How to Cite

    Blague , N. ., Ousman , B. ., Li Gwet David , L. ., Jean Claude , K. ., & Nelio , N. . (2025). 2D-filter design based on Volterra equation and machine learning ‎to tackle the aliasing effect in image demosicing. International Journal of Engineering and Technology, 14(1), 14-23. https://doi.org/10.14419/50xc1e97

    Received date: January 23, 2025

    Accepted date: March 19, 2025

    Published date: March 20, 2025