This paper deals with a novel nonlinear coupled nonlocal reaction-diffusion system proposed for image restoration, characterized by the advantages of preserving low gray level features and textures.The gray level indicator in the proposed model is regularized using a new method based on porous media type equations, which is suitable for recovering noisy blurred images. The well-posedness, regularity, and other properties of the model are investigated, addressing the lack of theoretical analysis in those existing similar types of models. Numerical experiments conducted on texture and satellite images demonstrate the effectiveness of the proposed model in denoising and deblurring tasks.

翻译：本文研究一种用于图像复原的新型非线性耦合非局部反应-扩散系统，其特点在于能够有效保持低灰度特征与纹理结构。该模型中灰度指示函数通过基于多孔介质型方程的新方法进行正则化，适用于含噪模糊图像的复原。本文深入探讨了模型的适定性、正则性及其他数学性质，弥补了现有同类模型理论分析不足的缺陷。在纹理图像与卫星图像上进行的数值实验表明，所提模型在去噪与去模糊任务中具有显著有效性。