Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models

In image processing, the Rudin-Osher-Fatemi (ROF) model [L. Rudin, S. Osher, and E. Fatemi, Physica D, 60(1992), pp. 259–268] based on total variation (TV) minimization has proven to be very useful. A lot of efforts have been devoted to obtain fast numerical schemes and overcome the non-differentiability of the model. Methods considered to be particularly efficient for the ROF model include the dual methods of Chan-Golub-Mulet (CGM) [T.F. Chan, G.H. Golub, and P. Mulet, SIAM J. Sci. Comput., 20(1999), pp. 1964–1977] and Chambolle [A. Chambolle, J. Math. Imaging Vis., 20(2004), pp. 89–97], and splitting and penalty based method [Y. Wang, J. Yang, W. Yin, and Y. Zhang, SIAM J. Imaging Sciences, 1(2008), pp. 248–272], as well as split Bregman iteration [T. Goldstein, and S. Osher, SIAM J. Imaging Sciences, 2(2009), pp. 323–343]. In this paper, we propose to use augmented Lagrangian method to solve the model. Convergence analysis will be given for the method. In addition, we ob...

• Type: Journal
• Year: 2010
• Where: SIAMIS
• Authors: Chunlin Wu, Xue-Cheng Tai
• Keywords: Bregman Iteration, Dual Method, SIAM J, SIAMIS 2010