Image denoising and enhancement based on adaptive fractional calculus of small probability strategy

•The optimal order of each pixel is selected based on the local average gradient.•The appearance of noise points is regarded as small probability events.•We use the improved two-dimensional Otsu algorithm to segment images.•The function of order vv is constructed based on the features of image areas.•AFC-SPS algorithm can remove noise and enhance image edge simultaneously.

This paper presents two methods to deal with the problem that traditional image denoising algorithms may easily neglect image texture details. The first one is global adaptive fractional integral algorithm (GAFIA) which deals with common noises. It selects the optimal integral order of each pixel based on the local average gradient. The second is image denoising and enhancement algorithm based on adaptive fractional calculus of small probability strategy (AFC-SPS) which deals with salt & pepper noise. It regards the appearance of noise points as small probability events, divides them, and segments the image edges and weak textures by the improved two-dimensional Otsu algorithm. Then, the function of adaptive fractional order is constructed. Experimental results show that, both of the methods have good image denoising effect, and the AFC-SPS algorithm has a better effect than other methods in enhancing the edge and preserving the texture.