中文摘要：

基于对偶理论提出了一种用于图像去噪的原始对偶模型.从理论上分析了该模型与ROF（Rudin,Osher,Fatime）去噪模型的等价性,以及与具有鞍点结构的优化模型在结构上的相似性.使用一种求解鞍点问题的基于预解式的原始对偶算法对该模型进行求解,论证了确保算法收敛性的参数取值范围.在模型参数选取方面,基于Morozov偏差原理自适应选取调整参数,从而限制图像去噪寻优过程的可行域,保护图像特征.实验结果表明,提出的调整参数自适应选取策略能有效改善去噪效果,同时采用的基于预解式的原始对偶算法能有效快速收敛.

英文摘要：

A primal-dual model for image denoising is proposed based on duality principle. We theoretically analyze its equivalency with the ROF denoising model, and its structural similarity with the saddle-point optimization model. A primal-dual algorithm based on resolvent for solving the saddle-point problem is used for solving the model. To guarantee the convergence, the range of parameter is given. In terms of model＇s parameter selec- tion, the regularization parameter is updated adaptively based on the Morozov＇s discrepancy principle which can guarantee the denoised image in the feasible set, and protect more image feature. The experiment results show that the proposed regularization parameter selection strategy is effective in improving the denoising effect. Simultaneously, the primal-dual algorithm based on resolvent can convergent rapidly.