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.

中文翻译：

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一种用于乘法噪声去除的新型分数阶反应扩散系统

在本文中，提出了一种分数阶非线性反应扩散系统来去除乘法伽玛噪声。新的反应扩散系统由三个方程组成：正则化的 Perona 和 Malik (PM) 方程，用于对被噪声污染的图像进行预平滑；时延正则化方程，用于将过去的信息纳入扩散过程并调整过平滑；和分数阶扩散方程，用于去除乘法伽玛噪声和保持纹理。新的反应扩散系统是耦合的，导致理论分析的困难。为此，我们利用解耦和 Schauder 不动点定理得到系统弱解的存在唯一性。采用显式有限差分格式来实现分数阶非线性反应扩散系统。此外，我们测试了纹理图像和非纹理图像。实验结果表明，与其他三种模型相比，新模型在去噪性能和纹理保留之间取得了更好的平衡。