A New Newton Method for Anisotropic Diffusion Model in Image Denoising

摘要

The general solution of anisotropic diffusionmodel in image denoising has slow convergence rate. Toovercome the problem, a new Newton method is proposed. In the new model, first and second Gateaux derivatives are figured out firstly. Then two continuous operators are introduced to avoid the error which is arisen by directly discretizing the iteration equation. To solve the singularity problem of the image and eliminate the impact of parameter, image geometry feature is considered when computing the equation using lagged fixed pointalgorithm. The classical Rudin-Osher-Fatemi(ROF) model is taken as an example. In the numerical experiment, the denoising performance of the new Newton method is compared with gradient descent algorithm and the Newton method which is proposed by Vogel. The numerical results demonstrate that new algorithm has faster computing rate with similar denoising performance of traditional algorithms.