Tensor Completion through Total Variation with Initialization from Weighted HOSVD

In our paper, we have studied the tensor completion problem when the sampling pattern is deterministic. We first propose a simple but efficient weighted HOSVD algorithm for recovery from noisy observations. Then we use the weighted HOSVD result as an initialization for the total variation. We have proved the accuracy of the weighted HOSVD algorithm from theoretical and numerical perspectives. In the numerical simulation parts, we also showed that by using the proposed initialization, the total variation algorithm can efficiently fill the missing data for images and videos.