An improved fractional-order differentiation model for image denoising

• An improved fractional differential operator for image denoising is proposed.
• Our denoising filter operator mask based on G–L fractional is constructed.
• The total coefficient of filter mask is not equal to zero.
• This nonlinear filter mask can preserve the detail features while denoising.

This paper investigates fractional order differentiation and its applications in digital image processing. We propose an improved model based on the Grünwald-Letnikov (G–L) fractional differential operator. Our improved denoising operator mask is based on G–L fractional order differentiation. The total coefficient of this mask is not equal to zero, which means that its response value is not zero in flat areas of the image. This nonlinear filter mask enhances and preserves detailed features while effectively denoising the image. Our experiments on texture-rich digital images demonstrated the capabilities of the filter. We used the information entropy and average gradient to quantitatively compare our method to existing techniques. Additionally, we have successfully used it to denoise three-dimensional magnetic resonance images.