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. (C) 2018 Elsevier B.V. All rights reserved.