Improved image denoising through fractional anisotropic diffusion and resolution-tailored differentiation in the Fourier domain

Fractional-order anisotropic diffusion-based denoising of images has been implemented in the literature through fractional differentiation in the Fourier domain. Furthermore, Fourier transform of the schemes on half-integer or integer mesh points has been used for the differentiation of images. In this paper, differentiation in the Fourier domain is proposed using schemes on fractional mesh points, aiming to enhance the performance of the algorithm. This can be regarded as employing fractional schemes at various resolutions, governed by a parameter of resolution within the range of (0.5, 1). Variations in resolution affect the pixel neighborhood by incorporating additional information from interpolated pixels. Experiments conducted on a reference image dataset, using three quantitative measures, demonstrate that the proposed method surpasses the method from the literature for higher values of the parameter of resolution. The improvement is particularly noticeable at higher noise levels, where the proposed method consistently outperforms the method from the literature across all values of the parameter of resolution. As a side effect, the proposed method is less time-consuming than the original method, as it requires higher time steps within the numerical scheme. Experiments and stability analysis show that the proposed method reduces the number of iterations by three to four times compared to the original method.