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 [41] based method, such as linearized Bregman [42, 9, 10, 49] and split Bregman [31] . The convergence of the general algorithm framework is proved under mild assumptions. The applications to 1 basis pursuit, TV−L 2 minimization and matrix completion are demonstrated. Finally, the numerical examples show the algorithms proposed are easy to implement, efficient, stable and flexible enough to cover a wide variety of applications.
A unified primal-dual algorithm framework is proposed to resolve the local total variation problem with L 1 basis pursuit and TV-L 2 minimization REF .
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Mathematics Computer Science