We propose a new variational model for image denoising, which employs the L1-norm of the mean curvature of the image surface. Besides eliminating noise and preserving edges of objects efficiently, our model can keep corners of objects and greyscale intensity contrasts of images and also remove the staircase effect. We analytically study the proposed model and justify why our model can preserve object corners and image contrasts. We apply the proposed model to the denoising of curves and plane images, and also compare the results with those obtained by using the classical Rudin–Osher–Fatemi model. Finally, we present a fast computational method for our model using an augmented Lagrangian formulation.
(Joint work with Wei ZHU, Department of Mathematics, University of Alabama and Xue-Cheng Tai, Department of Mathematics, University of Bergen)