Multiplicative Noise Removal for Texture Images Based on Adaptive Anisotropic Fractional Diffusion Equations

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, multiplicative noise destroys almost all information of the original image, especially for texture images. In this paper, a fractional-order nonlinear diffusion model is proposed to denoise the texture images corrupted by multiplicative noise. In the model, a gray level indicator is introduced to remove multiplicative noise and preserve structure details for texture images. By virtue of the discrete Fourier transform, the model is solved by an iterative scheme in the frequency domain. Then an algorithm in the spatial domain is developed based on the definition of the Grunwald-Letnikov fractional-order derivative. Inspired by the discrepancy principle used for additive noise, we develop a new stopping criterion based on the mean and variance of the noise. Numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed method. Experimental results show that the proposed model can handle multiplicative noise removal and texture preservation quite well.