Image denoising based on fractional anisotropic diffusion and spatial central schemes

Abstract

Fractional-order anisotropic diffusion realized in the Fourier domain is a widely used model for image denoising. While fractional differentiation in the Fourier domain introduces a complex component, differentiation with central schemes in the spatial domain is preferred in image processing applications. This paper presents numerical solution to the fractional anisotropic diffusion equation in the spatial domain, using novel central fractional difference schemes. The proposed central schemes assume a two-part differentiation approach: an integer order, defined by the integer part of the order of differentiation, and a non-integer order, defined by the non-integer part. This approach allows the proposed schemes to incorporate integer-order calculus. The conducted stability analysis of the numerical schemes yields optimistic results regarding convergence conditions, demonstrating that the schemes are unconditionally stable for orders of differentiation greater than 0.5. The parameters of the proposed model are adjusted through a set of experiments that illustrate its performance. The proposed model is tested against counterpart models from the literature using an image dataset, and the obtained qualitative and quantitative results favor the proposed model across various noise levels.