Image Denoising via L2-Norm of Anisotropic Mean Curvature of Image Surface

This paper presents a novel variational model for image denoising, which employs the L2-norm of the anisotropic mean curvature (L2-AMC) of the image surface as a regularizer. In contrast to existing mean curvature-based approaches that employ the L1-norm, the L2 formulation provides stronger regularization, leading to more effective noise suppression and better preservation of fine structures and anisotropic features. To handle the resulting fourth-order, non-convex energy functional, we introduce auxiliary variables and develop an efficient solver based on the augmented Lagrangian method and the alternating direction method of multipliers (ADMM), which decomposes the problem into subproblems with closed-form or FFT-based solutions. Numerical experiments on Set12 dataset and the Texmos image under additive Gaussian white noise demonstrate that the proposed approach achieves competitive denoising performance and compares favorably with the other variational methods in terms of both visual quality and quantitative metrics.