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Noise detection and image denoising based on fractional calculus

Author

Listed:
  • Wang, Qi
  • Ma, Jing
  • Yu, Siyuan
  • Tan, Liying

Abstract

Fractional-order integral can weaken high-frequency signal and greatly preserve low-frequency signal nonlinearly, that is, the high-frequency noise can be removed while retaining the information of low-frequency image itself, thus the fractional calculus can achieve good a denoising effect and the application of fractional calculus theory in the digital image processing field has also been favored by more and more scholars. On the basis of summarizing and analyzing previous research works, this paper proposes a new method for detecting noise points in images using fractional differential gradient and an improved image denoising algorithm based on fractional integration. The noise detection method determines the noise position by the fractional differential gradient, and achieves to detect the noise, snowflake and stripe anomaly though utilizing the neighborhood information feature of the image and the contour and direction distribution of various noise anomalies in spatial domain; the image denoising algorithm firstly regards the appearance of noise points in image as a small probability event and divides it, then applies the fractional calculus to subtly transform and adjust signal filter and meanwhile utilizes iterative idea to control image denoising effect for accurately distinguishing between noise and high-frequency signals, so that the original image feature information is more preserved while the image is denoised. The simulation results show that this algorithm model can effectively remove the noise while maintaining the details of image edge and texture, and have the characteristics of simple algorithm and good stability. The model can effectively remove the noise and meanwhile preserve the details of image edges and textures, and has the characteristics of simple algorithm and high stability. The study results of this paper provide a reference for further research on the noise detection and image denoising based on fractional calculus.

Suggested Citation

  • Wang, Qi & Ma, Jing & Yu, Siyuan & Tan, Liying, 2020. "Noise detection and image denoising based on fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304096
    DOI: 10.1016/j.chaos.2019.109463
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    References listed on IDEAS

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    1. Yi-Ting Chen & Wan-Ni Lai & Edward W. Sun, 2019. "Jump Detection and Noise Separation by a Singular Wavelet Method for Predictive Analytics of High-Frequency Data," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 809-844, August.
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    Cited by:

    1. Peng, Qiu & Jian, Jigui, 2023. "Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Wu, Kai & Tang, Ming & Ren, Han & Zhao, Liang, 2023. "Quantized pinning bipartite synchronization of fractional-order coupled reaction–diffusion neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Poonam Pawar & Bharati Ainapure & Mamoon Rashid & Nazir Ahmad & Aziz Alotaibi & Sultan S. Alshamrani, 2022. "Deep Learning Approach for the Detection of Noise Type in Ancient Images," Sustainability, MDPI, vol. 14(18), pages 1-19, September.

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