中文摘要：

针对总变分去噪模型容易导致阶梯效应的缺陷，提出了一种新的乘性噪声去噪模型。在新模型中，二阶总广义变分（TGV）是正则项，它能自动平衡一阶和二阶导数项，使得新模型在去除乘性噪声的同时不但能够保持图像的边缘信息，而且还能去除阶梯效应。为了有效的计算该模型，设计了一个快速迭代算法。在算法中，首先采用分裂方法和交替方向法将原问题变为两个相关的子问题，然后分别对子问题利用牛顿法和原始一对偶算法。实验结果表明，与同类模型相比，本文方法无论是在视觉效果还是定量指标，如峰值信噪比（PSNR）等都有明显地提高。

英文摘要：

Aiming at the drawback of the total variational denoising model in which the staircase effect is often produced,an improved multiplicative noise removal model based on second-order total generalized variation （TGV） is proposed in this paper. In this new model, the second-order total generalized variation is the regularization term,which can automatically balance the first order derivative and the second order derivative. So the proposed model makes use of the characteristics of second total generalized variation which makes the edges in the restored image preserved well and removes multiplicative noise while avoiding the staircase effect. In order to solve the proposed model effectively, a fast iteration algorithm is designed. In the algorithm,we first use the splitting method and alternating direction method to divide the primal problem into two relevant subproblems, and then the Newton method and primal-dual method are adopted in the respective subproblem. The comprehensive experimental results show that compared with the existing congeneric algorithms, the new model is more effective to filter out the existing multiplicative noise and preserves the edges of image while avoiding the staircase effect. Therefore, the restored results are improved in both visual effects and some quantitative indexes, such as peak signal to noise ratio.