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Image restoration method based on fractional variable order differential

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Abstract

In this paper, we study image restoration problem by using fractional variable order differential technique. Our idea is to make use of fractional order differential diffusion equation of evolution procedure into the image restoration problem. An image often exists different low-frequency and high-frequency components, such as flat, texture and edge, etc. Because fractional order differential can enhance the high-frequency components of a signal, meanwhile, nonlinearly preserve the low-frequency components of the signal, we can adapt suitable fractional differential orders to restore their components. In particular, different differential orders can be used in an image at the same time. In order to obtain the restored image automatically, we choose the fractional differential orders by the value of gradient modulus of the image and use the discrete Fourier transform to implement the numerical algorithm. We also provide an iterative scheme in the frequency domain. Experimental results are reported to demonstrate that the visual effects, the combined image similarity index and the peak signal to noise ratio of restored images by using the proposed method are very good, and are competitive with the other testing methods.

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Authors and Affiliations

  1. College of Information Science and Technology, Hainan University, Haikou, China

    Yan-Shan Zhang

  2. Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China

    Feng Zhang

  3. Department of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China

    Bing-Zhao Li

Authors
  1. Yan-Shan Zhang
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  2. Feng Zhang
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  3. Bing-Zhao Li
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Corresponding author

Correspondence to Feng Zhang.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grants Nos. 61571042, 61331021 and 61421001. We acknowledge the financial support from the China Scholarship Council.

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Zhang, YS., Zhang, F. & Li, BZ. Image restoration method based on fractional variable order differential. Multidim Syst Sign Process 29, 999–1024 (2018). https://doi.org/10.1007/s11045-017-0482-z

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  • DOI: https://doi.org/10.1007/s11045-017-0482-z

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