  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.
