A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration

• DOI: 10.1007/s10915-010-9408-8
• Publication Date: 2010-08-04T20:15:47Z
• Authors: Xiaoqun Zhang; Martin Burger; Stanley Osher
• Keywords: Bregman divergence; Minification; Matrix (chemical analysis)

In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications. We also show the connections to existing methods, in particular Bregman iteration (Osher et al., Multiscale Model. Simul. 4(2):460–489, 2005) based such as linearized Commun. Math. Sci. 8(1):93–111, 2010; Cai SIAM J. Imag. 2(1):226–252, 2009, CAM Report 09-28, UCLA, March 2009; Yin, CAAM Report, Rice University, 2009) split (Goldstein Osher, Sci., 2, 2009). The convergence general is proved under mild assumptions. applications ℓ 1 basis pursuit, TV−L 2 minimization matrix completion are demonstrated. Finally, numerical examples algorithms proposed easy implement, efficient, stable flexible enough cover wide variety