Image denoising algorithm based on the convolution of fractional Tsallis entropy with the Riesz fractional derivative

Abstract

Image denoising is an important component of image processing. The interest in the use of Riesz fractional order derivative has been rapidly growing for image processing recently. This paper mainly introduces the concept of fractional calculus and proposes a new mathematical model in using the convolution of fractional Tsallis entropy with the Riesz fractional derivative for image denoising. The structures of n × n fractional mask windows in the x and y directions of this algorithm are constructed. The image denoising performance is assessed using the visual perception, and the objective image quality metrics, such as peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). The proposed algorithm achieved average PSNR of 28.92 dB and SSIM of 0.8041. The experimental results prove that the improvements achieved are compatible with other standard image smoothing filters (Gaussian, Kuan, and Homomorphic Wiener).

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Acknowledgments

This research is funded by the Ministry of Higher Education Malaysia under the Fundamental Research Grant Scheme (FRGS), Project No.: FP073-2015A.

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All authors jointly worked on deriving the results and approved the final manuscript.

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Correspondence to Hamid A. Jalab.

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The authors declare that there are no conflict of interests regarding the publication of this article.

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Jalab, H.A., Ibrahim, R.W. & Ahmed, A. Image denoising algorithm based on the convolution of fractional Tsallis entropy with the Riesz fractional derivative. Neural Comput & Applic 28, 217–223 (2017). https://doi.org/10.1007/s00521-016-2331-7

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Keywords

  • Fractional calculus
  • Fractional mask
  • Fractional Tsallis entropy
  • Riesz fractional derivative