Augmented Lagrangian method for a mean curvature based image denoising model

High order derivative information has been widely used in developing variational models in image processing to accomplish more advanced tasks. However, it is a nontrivial issue to construct efficient numerical algorithms to deal with the minimization of these variational models due to the associated high order Euler-Lagrange equations. In this paper, we propose an efficient numerical method for a mean curvature based image denoising model using the augmented Lagrangian method. A special technique is introduced to handle the mean curvature model for the augmented Lagrangian scheme. We detail the procedures of finding the related saddle-points of the functional. We present numerical experiments to illustrate the effectiveness and efficiency of the proposed numerical method, and show a few important features of the image denoising model such as keeping corners and image contrast. Moreover, a comparison with the gradient descent method further demonstrates the efficiency of the proposed augmented Lagrangian method.