Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 363–390 | Cite as

Generalized Fractional Filter-Based Algorithm for Image Denoising

  • Anil K. Shukla
  • Rajesh K. PandeyEmail author
  • Swati Yadav
  • Ram Bilas Pachori


This paper presents a new algorithm for image denoising using a fractional integral mask of the K-operator. K-operator is the generalized fractional operator, and it reduces to Riemann–Liouville and Caputo fractional derivatives in a special case. The proposed algorithm is applied to digital images of different nature to demonstrate the performance of image denoising. Experimental results are compared with other existing filters together with block matching and 3-D filtering, and weighted nuclear norm minimization-based approaches. The obtained experimental results show that the proposed algorithm is computationally efficient and its average performance is comparatively better than other discussed methods.


Fractional calculus Difference equations Interpolation Texture Image denoising 



The authors sincerely thank the Editor and reviewers for their constructive comments to improve the quality of the manuscript.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (BHU)VaranasiIndia
  2. 2.Discipline of Electrical EngineeringIndian Institute of Technology IndoreIndoreIndia

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