A texture image denoising approach based on fractional developmental mathematics

The traditional integer-order computation-based denoising approaches often blur the edges and textural details of an image. To solve this problem, from the viewpoint of system evolution, and based on the features of fractional calculus, we propose to implement a texture image denoising approach based on fractional developmental mathematics (FDM) which applies a novel mathematical method, fractional calculus, to image denoising. First, we synopsize the necessary theoretical background of fractional calculus. Second, we derive the necessary mathematical models for implementation of a texture image denoising approach based on FDM. We derive fractional Green’s formula, fractional Gauss’ formula, and fractional Stokes’ formula, and fractional Euler–Lagrange equation. Then, a texture image denoising approach based on FDM is proposed. Third, we implement comparative experiments. We firstly derive the numerical implementation of FDM. Then, we study the capability of preserving the edges and textural details of FDM by comparative experiments. The comparative experimental results show that the capability of preserving the edges and textural details of the FDM-based denoising algorithm is obviously superior to that of traditional integer-order computation-based algorithms, especially for texture detail rich images.