High order derivative information has been widely used in developing variational models in image processing to accomplish more advanced tasks. In this talk, we will discuss a variational model for image denoising using a second order regularization term, that is, the L1 norm of the mean curvature of the image surface for a given image. Besides eliminating noise and preserving edges of objects, the reguaralizer helps keep sharp corners and image contrasts and also remove the staircase effect. Due to the high order of the regularizer as well as its nondifferentiabilty and nonlinearity, it is nontrivial to develop efficient algorithms to minimize the proposed functional. In this talk, we will also discuss a fast algorithm using the augmented Lagrangian method for the associated minimization problem. We will present numerical experiments to show the properties of the image denoising model, to compare it with some classic models such as the Rudin-Osher-Fatemi model and Euler’s elastica based models, and validate the efficiency of the proposed fast algorithm.