Color image completion using tensor truncated nuclear norm with l0 total variation

In recent years, the problem of incomplete data has been behind the appearance of several completion methods and algorithms. The truncated nuclear norm has been known as a powerful low-rank approach both for the matrix and the tensor cases. However, the low-rank approaches are unable to characterize some additional information exhibited in data such as the smoothness or feature-preserving properties. In this work, a tensor completion model based on the convex truncated nuclear norm and the nonconvex-sparse total variation is introduced. Notably, we develop an alternating minimization algorithm that combines the accelerating proximal gradient for the convex step and a projection operator for the nonconvex step to solve the optimization problem. Experiments and comparative results show that our algorithm has a significant impact on the completion process.