Fractional-order Diffusion based Image Denoising Model

Abstract

Edge indicating operators such as gradient, mean curvature, and Gauss curvature-based image noise removal algorithms are incapable of classifying edges, ramps, and flat areas adequately. These operators are often affected by the loss of fine textures. In this paper, these problems are addressed and proposed a new coefficient of diffusion for noise removal. This new coefficient consists of two edge indicating operators, namely fractional-order difference curvature and fractional-order gradient. The fractional-order difference curvature is capable of analyzing flat surfaces, edges, ramps, and tiny textures. The fractional-order gradient can able to distinguish texture regions. The selection of the order is more flexible for the fractional order gradient and fractional-order difference curvature. This will result in effective image denoising. Since the discrete Fourier transform is simple to numerically implement, it is taken into consideration for the implementation of fractional-order gradient. The proposed method can give results that are visually appealing and improved quantitative outputs in terms of the Figure of Merit (FoM), Mean Structural Similarity (MSSIM), and Peak Signal to Noise Ratio (PSNR), according to comparative analysis.