A novel fractional‐order reaction diffusion system for the multiplicative noise removal

Abstract In this paper, a fractional‐order nonlinear reaction diffusion system is proposed to remove the multiplicative Gamma noise. The new reaction diffusion system consists of three equations: the regularized Perona and Malik (PM) equation , which is used for presmoothing the image that is contaminated by noise; the time‐delay regularization equation, which is used for incorporating the past information into the diffusion process and adjusting oversmoothing; and the fractional‐order diffusion equation, which is used for removing the multiplicative Gamma noise and maintaining texture. The new reaction diffusion system is coupled, leading to the difficulty in theoretical analysis. To this end, we use decoupled and Schauder's fixed‐point theorem to obtain the existence and uniqueness of weak solution of the system. The explicit finite difference scheme is employed to implement the fractional‐order nonlinear reaction diffusion system. In addition, we test both texture images and nontexture images. Experimental results show that the new model achieves a better trade‐off between denoising performance and texture preservation than the other three models.