The mean curvature (MC)-based image denoising and image deblurring models are used to enhance the quality of the denoised images and deblurred images respectively. These models are very efficient in removing staircase effect, preserving edges and other nice properties. However, high order derivatives appear in the Euler–Lagrange equations of the MC-based models which create problems in developing an efficient numerical algorithm. To overcome this difficulty, we present a robust and efficient Two-Level method for MC-based image denoising and image deblurring models. The Two-Level method consists of solving one small problem and one large problem. The small problem is a nonlinear system, having high order derivative, on Level I (image having small number of pixels). The large problem is one less expensive system, having low order derivative, on Level II (image having large number of pixels). The derivation of the optimal regularization parameter of Level II is studied and formula is presented. Numerical experiments on digital images are presented to exhibit the performance of the Two-Level method.

基于平均曲率（MC）的图像去噪和图像去模糊模型分别用于提高去噪图像和去模糊图像的质量。这些模型在消除阶梯效应、保留边缘和其他良好属性方面非常有效。然而，高阶导数出现在基于 MC 的模型的欧拉-拉格朗日方程中，这在开发有效的数值算法时产生了问题。为了克服这个困难，我们为基于 MC 的图像去噪和图像去模糊模型提出了一种鲁棒且高效的两级方法。两级方法包括解决一个小问题和一个大问题。小问题是一个非线性系统，在级别 I（具有少量像素的图像）上具有高阶导数。最大的问题是一个成本较低的系统，具有低阶导数，在 II 级（具有大量像素的图像）。研究了Level II最优正则化参数的推导，并给出了公式。提出了数字图像的数值实验来展示两级方法的性能。