Signal, Image and Video Processing

, Volume 6, Issue 3, pp 503–511 | Cite as

1-D and 2-D digital fractional-order Savitzky–Golay differentiator

  • Dali Chen
  • YangQuan ChenEmail author
  • Dingyu Xue
Original Paper


In this paper, the one-dimension digital fractional-order Savitzky–Golay differentiator (DFOSGD), which generalizes the Savitzky–Golay filter from the integer order to the fractional order, is introduced and extended to 2-D by a group of direction operators. Then, a new image-enhancing algorithm is proposed based on the 2-D DFOSGD, and an unsupervised optimization algorithm is proposed for choosing the fractional-order parameter. Four numerical experiments are used to assess the performance of 2-D DFOSGD-based image-enhancing algorithm, and the results demonstrate its validity.


Fractional-order derivative Digital differentiator Savitzky–Golay filter Image enhancement 


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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.College of Information Science and EngineeringNortheastern UniversityShenyangChina
  2. 2.Department of Electrical and Computer Engineering, Center for Self-Organizing and Intelligent Systems (CSOIS)Utah State UniversityLoganUSA

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