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

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.

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