The curvature regularization method is well-known for its good geometric interpretability and strong priors in the continuity of edges, which has been applied to various image processing tasks. However, due to the non-convex, non-smooth, and highly non-linear intrinsic limitations, most existing algorithms lack a convergence guarantee. This paper proposes an efficient yet accurate scalar auxiliary variable (SAV) scheme for solving both mean curvature and Gaussian curvature minimization problems. The SAV-based algorithms are shown unconditionally energy diminishing, fast convergent, and very easy to be implemented for various image processing tasks. Numerical experiments on Gaussian noise removal, mixed noises removal, image deblurring, and single image super-resolution are presented on both gray and color image datasets to demonstrate the robustness and efficiency of our method. @inproceedings{ title={ Efficient-SAV-Algorithms-for-Curvature-Minimization-Problems},
author={Chenxin Wang1, Zhenwei Zhang1, Zhichang Guo, Tieyong Zeng, and Yuping Duan∗},
year={2022} }