A novel image denoising approach based on a curvature-based regularization

The classical total variation (TV) model has made great successes in image denoising due to the edge-preserving property of the TV regularization. However, it is well known that the TV model suffers from the staircase effects and the loss of image details. In order to overcome these problems, high-order variational models have been widely used to yield better quality of denoised images. In this paper, we first propose a new high-order image denoising model based on the sum of squared principal curvatures of the image surface of a given image. As a result, the associated Euler–Lagrange equation is highly nonlinear and of fourth order so standard numerical techniques such as gradient descent methods are not appropriate. We therefore propose an efficient numerical solution using the split Bregman (SB) method. Numerical tests not only show that the proposed curvature model is more robust in removing noise and preserving structural information for a wide range of applications than some existing high-order variational models, but also that the proposed numerical solution is accurate in delivering visually pleasing results.