Fractional-order diffusion model for multiplicative noise removal in texture-rich images and its fast explicit diffusion solving (Q2100540)

A fractional-order anisotropic diffusion model, based on fractional Fick's law for multiplicative noise removal in texture-rich images, is proposed. A fast explicit diffusion solving algorithm is considered. It is shown that the new model is different from the model derived from the fractional-order variation method and arises from a physical consideration. For actual numerical applications, the discrete Grünwald-Letnikov approximation is employed to implement the finite difference discretization of the model, yielding a dense coefficient matrix. Limited nodes are used in the Grünwald-Letnikov approximation to produce a sparse coefficient matrix for computational tractability, while the fast explicit diffusion method is used to speed up the computations. The performance of the proposed model is illustrated by comparing it with other denoising models studied in the literature.