Multiplicative noise removal based on total generalized variation

Abstract

© Springer Nature Singapore Pte Ltd. 2018. When the first order variational models are used for multiplicative noise removal, there always some staircase effect, contract reduction, and corner smearing. In this paper, we will design a new second order variational model based on the total generalized variation (TGV) regularizer to solve these problems. The second order variation model is proposed originally for additive noise removal and we revise it in this paper for multiplicative noise removal. For the sake of computational efficiency, we transform this proposed model into a Split Bregman iterative scheme by introducing some auxiliary variables and iterative parameters, and then solve it via alternating optimization strategy. In order to speed up the computational efficiency, we also apply the fast Fourier transform (FFT), generalized soft threshold formulas and gradient descent method to the related sub-problems in each step. The experimental results show that in comparison with the first order total variation (TV) model, the proposed TGV model can effectively overcome the staircase effect; Also in comparison with the second order bounded Hessian regularization, the TGV model shows the advantage of preserving corners and edges in images.