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 based method, such as linearized Bregman and split Bregman. The convergence of the general algorithm framework is proved under mild assumptions. The applications to l1 basis pursuit, TV-L2 minimization, nonlocal 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.
L'exposé sera en français