In order to improve the effect of image enhancement, A new method of image enhancement was presented in this paper. Firstly, this method in this paper inherited the fine characteristics of the traditional fractional order differential, and broke the idea to take an unit step in G-L definition to use non-integer step, which increased the accuracy of the fractional order differential numerical calculation. What’s more, the method utilized the linear weighting method based on Lagrange polynomial section interpolation to determine the gray values of the non-integer step pixel. To a certain extent, it could play a role in noise reduction. Therefore, the method proposed in this paper had made a better balance between enhancing the image details and denoising. The experimental results shew that in the noise-free case, the method proposed in this paper compared with the traditional fractional differential operator in the image enhancement was better; in a noise case, the method had a certain amount of noise immunity.
