论文标题
一种对称交替的最小化算法，用于最小化
A symmetric alternating minimization algorithm for total variation minimization
论文作者
论文摘要
在本文中，我们提出了一种新型的对称交替最小化算法，以解决一类广泛的总变异（TV）正则化问题。与通常的$ z^k \至x^k $ gauss-seidel循环不同，所提出的算法执行特殊$ \ overline {x}^{k} {k} \ to z^k \ to z^k \ to x^k $ cycle。我们设置的主要思想是用于解决多块凸复合问题的最新对称高斯 - 塞德尔（SGS）技术。这个想法还使我们能够建立所提出的方法与众所周知的加速近端梯度（APG）方法之间的等效性。可以直接从APG框架和数值结果中直接获得所提出算法的更快收敛速率，包括图像降解，图像脱毛和分析稀疏恢复问题证明了新算法的有效性。
In this paper, we propose a novel symmetric alternating minimization algorithm to solve a broad class of total variation (TV) regularization problems. Unlike the usual $z^k\to x^k$ Gauss-Seidel cycle, the proposed algorithm performs the special $\overline{x}^{k}\to z^k\to x^k$ cycle. The main idea for our setting is the recent symmetric Gauss-Seidel (sGS) technique which is developed for solving the multi-block convex composite problem. This idea also enables us to build the equivalence between the proposed method and the well-known accelerated proximal gradient (APG) method. The faster convergence rate of the proposed algorithm can be directly obtained from the APG framework and numerical results including image denoising, image deblurring, and analysis sparse recovery problem demonstrate the effectiveness of the new algorithm.
