Fractional-order difference curvature-driven fractional anisotropic diffusion equation for image super-resolution

Abstract

Image super-resolution methods-based existing edge indicating operators — namely Gauss curvature, mean curvature and gradient — cannot effectively identify the edges, ramps and flat regions and suffer from the loss of fine textures. To address these issues, this paper presents a fractional anisotropic diffusion equation based on a new edge indicator, named fractional-order difference curvature, which can characterize the intensity variations in images. We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform, which is easy to implement numerically. The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures. Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.