Neural Computing and Applications

, Volume 28, Supplement 1, pp 217–223 | Cite as

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

  • Hamid A. JalabEmail author
  • Rabha W. Ibrahim
  • Amr Ahmed
Original Article


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).


Fractional calculus Fractional mask Fractional Tsallis entropy Riesz fractional derivative 



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

Author contributions

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

Compliance with ethical standards

Conflict of interest

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


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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  1. 1.Faculty of Computer Science and Information TechnologyUniversity MalayaKuala LumpurMalaysia
  2. 2.Lincoln School of Computer ScienceUniversity of LincolnLincolnUK

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