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.

中文翻译：

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一种用于总变异最小化的对称交替最小化算法

在本文中，我们提出了一种新颖的对称交替最小化算法来解决广泛的总变分 (TV) 正则化问题。与通常的 $z^k\to x^k$ 高斯-赛德尔循环不同，该算法执行特殊的 $\overline{x}^{k}\to z^k\to x^k$ 循环。我们设置的主要思想是最近为解决多块凸复合问题而开发的对称高斯-赛德尔 (sGS) 技术。这个想法还使我们能够在所提出的方法和众所周知的加速近端梯度 (APG) 方法之间建立等效性。该算法较快的收敛速度可以直接从APG框架中获得，包括图像去噪、图像去模糊、分析稀疏恢复问题在内的数值结果证明了新算法的有效性。