A simple primal-dual algorithm for nuclear norm and total variation regularization

We propose a simple primal-dual method for nuclear norm plus total variation minimization problems. A predictor-corrector scheme to the dual variable is used in our algorithm. Convergence of the method is proved and convergence rate which is O(1/N) in the ergodic sense is also discussed, where N denotes the iteration number. Numerical results including tensor completion, parallel magnetic resonance imaging and dynamic magnetic resonance imaging demonstrate the efficiency of the new algorithm.