Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal

Abstract

The problem of multiplicative noise removal has attracted much attention in recent years. Unlike additive noise, multiplicative noise destroys almost all information of an image; therefore, it is more difficult to remove them from corrupted images. In this paper, we propose a denoising model of fractional-order diffusion coupled with integer-order diffusion for multiplicative gamma noise, which takes advantage of both texture-preserving property of fractional-order diffusion and edge-preserving property of integer-order diffusion. We explore the mutual mechanism of two diffusion equations in the diffusion process, i.e., mutual transfer of texture and edge information respectively from two filtering images, and mutual regularization on the diffusion coefficients in both equations. We design an alternating numerical scheme based on semi-implicit finite difference and discrete Fourier transform for solving the coupled diffusion system. The proposed model is tested on some commonly-used images and is compared with six state-of-the-art models, qualitatively and quantitatively. Experimental results show the superiority of the proposed model in reducing multiplicative gamma noise while preserving textures and edges.