A new and efficient fixed point method for mean curvature denoising model

Abstract

The mean curvature model is one of the efficient higher-order models for image denoising, and its Euler-Lagrange equation is a fourth-order nonlinear equation which makes the development of efficient numerical methods very difficult. In this paper, on the one hand, it is proposed to replace the gradient in the nonlinear terms other than the mean curvature with the gradient obtained by convolving the image with a Gaussian low-pass filter. This modification leads to a new Euler-Lagrange equation that retains the structure of the original equation, but with a reduced degree of nonlinearity. On the other hand, we also develop a novel fixed point curvature method to solve this new equation. Numerical experiments show that our method not only recovers high-quality images from highly noisy images, but is also 10 times faster than the nonlocal means (NLM) method and 6–10 times faster than the the augmented Lagrangian method.