Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite optimization problem solvable by a variety of primal dual-type methods. We propose a fair primal dual algorithmic framework that incorporates the smooth term not only into the primal subproblem but also into the dual subproblem. We unify the global convergence and establish the convergence rates of our proposed fair primal dual method. Experiments on image denoising and super-resolution reconstruction demonstrate the superiority of the proposed method over the current state-of-the-art.

翻译：图像逆问题在图像处理、超分辨率及计算机视觉等领域具有广泛应用，这些领域是图像科学的重要研究方向。此类应用模型可视为三函数复合优化问题，可通过多种原始对偶类方法求解。本文提出一种公平原始对偶算法框架，将光滑项同时纳入原始子问题与对偶子问题的求解过程。我们统一证明了该方法的全局收敛性，并建立了公平原始对偶方法的收敛速率。在图像去噪与超分辨率重建任务上的实验表明，所提方法优于当前最先进技术。