Fast smooth rank approximation for tensor completion

In this paper we consider the problem of recovering an N-dimensional data from a subset of its observed entries. We provide a generalization for the smooth Shcatten-p rank approximation function in [1] to the N-dimensional space. In addition, we derive an optimization algorithm using the Augmented Lagrangian Multiplier in the N-dimensional space to solve the tensor completion problem. We compare the performance of our algorithm to state-of-the-art tensor completion algorithms using different color images and video sequences. Our experimental results showed that the proposed algorithm converges faster (approximately half the execution time), and at the same time it achieves comparable performance to state-of-the-art tensor completion algorithms.