In this paper, we propose image restoration models using optimal transport (OT) and total variation regularization. We present theoretical results of the proposed models based on the relations between the dual Lipschitz norm from OT and the G-norm introduced by Yves Meyer. We design a numerical method based on the Primal-Dual Hybrid Gradient (PDHG) algorithm for the Wasserstain distance and the augmented Lagrangian method (ALM) for the total variation, and the convergence analysis of the proposed numerical method is established. We also consider replacing the total variation in our model by one of its modifications developed in \cite{zhu}, with the aim of suppressing the stair-casing effect and preserving image contrasts. Numerical experiments demonstrate the features of the proposed models.

翻译：本文提出了一种结合最优传输与全变差正则化的图像复原模型。我们基于最优传输中的对偶Lipschitz范数与Yves Meyer提出的G-范数之间的关联性，建立了所提模型的理论分析框架。针对Wasserstein距离项，我们设计了基于原始-对偶混合梯度算法的数值求解方法；针对全变差项，则采用增广拉格朗日法进行优化，并对该数值方法的收敛性进行了理论证明。此外，我们还探讨了用\cite{zhu}中提出的改进全变差形式替代原模型中的标准全变差项，以期在抑制阶梯效应的同时更好地保持图像对比度。数值实验验证了所提模型的特性和有效性。