A novel partial differential equation (PDE)—based mixed image noise removal technique is proposed in this article. The considered approach filters successfully the images corrupted by combined Poisson–Gaussian noise by using a nonlinear fourth-order PDE-based denoising model that is proposed and carefully investigated here. Thus, a rigorous mathematical treatment of the validity of this model is performed, the existence of a weak solution of it being demonstrated. Then, the nonlinear PDE model is solved numerically by constructing a stable and fast-converging finite difference-based approximation scheme that is consistent to it. Mixed noise reduction experiments illustrating the effectiveness of the proposed approach are also discussed.

本文提出了一种新的基于偏微分方程 (PDE) 的混合图像噪声去除技术。所考虑的方法通过使用在此提出并仔细研究的基于非线性四阶偏微分方程的去噪模型成功地过滤了被组合泊松-高斯噪声破坏的图像。因此，对该模型的有效性进行了严格的数学处理，并证明了其弱解的存在。然后，通过构建与其一致的稳定且快速收敛的基于有限差分的近似方案，对非线性 PDE 模型进行数值求解。还讨论了说明所提出方法的有效性的混合降噪实验。