General nonconvex total variation and low-rank regularizations: Model, algorithm and applications

Total Variation and Low-Rank regularizations have shown significant successes in machine learning, data mining, and image processing in past decades. This paper develops the general nonconvex composite regularized model, which contains previous regularizers and motivates novel ones. Although the classical Alternating Direction Methods of Multiplier (ADMM) algorithm is applicable for this model, the nonconvexity of the problem and the complicacy of choosing the parameters increase the difficulty in the use of ADMM. Thus, by the penalty method, we propose the Alternating Minimization (AM) algorithm, whose convergence results are proved under mild assumptions. The proposed model and algorithm are applied to the image restoration problem. Numerical results demonstrate the efficiency of our model and algorithm.