A Fourth Order Dual Method for Iteration Regularization with H-1 Fidelity Based Denoising

Abstract

In this paper, we propose iterative regularization for image denoising problems, based on the total variation minimizing models proposed by Rudin, Osher, and Fatemi(ROF). Besides, considering the staircase occuring in the process of denoising, we combine the higher order derivatives, and use iterative scheme. The fourth order dual method is used to solve the minimization problems. The numerical experiments show the iterative procedure preserves more details and reduces staircasing. Besides, it can be claimed that the fourth order dual method is more faster and stable than time marching algorithms.