IEEE Trans Image Process. 2019 Dec;28(12):6211-6224. doi: 10.1109/TIP.2019.2924339. Epub 2019 Jun 27.
In image processing, total variation (TV) regularization models are commonly used to recover the blurred images. One of the most efficient and popular methods to solve the convex TV problem is the alternating direction method of multipliers (ADMM) algorithm, recently extended using the inertial proximal point method. Although all the classical studies focus on only a convex formulation, recent articles are paying increasing attention to the nonconvex methodology due to its good numerical performance and properties. In this paper, we propose to extend the classical formulation with a novel nonconvex alternating direction method of multipliers with the inertial technique (IADMM). Under certain assumptions on the parameters, we prove the convergence of the algorithm with the help of the Kurdyka-Łojasiewicz property. We also present numerical simulations on the classical TV image reconstruction problems to illustrate the efficiency of the new algorithm and its behavior compared with the well-established ADMM method.
在图像处理中，总变差（TV）正则化模型通常用于恢复模糊图像。解决凸 TV 问题最有效和最流行的方法之一是交替方向乘子法（ADMM）算法，最近使用惯性近端法进行了扩展。尽管所有经典研究都只关注凸公式，但由于其良好的数值性能和特性，最近的文章越来越关注非凸方法。在本文中，我们提出通过具有惯性技术的新颖非凸交替方向乘子法（IADMM）来扩展经典公式。在参数的某些假设下，我们借助 Kurdyka-Łojasiewicz 性质证明了算法的收敛性。我们还对经典 TV 图像重建问题进行了数值模拟，以说明新算法的效率及其与成熟的 ADMM 方法的行为比较。
