Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
This work addresses the challenge of fast and scalable tensor completion for image and video inpainting, offering significant performance improvements over existing methods.
The paper tackles the problem of tensor completion for images and videos by proposing a method based on tensor trains with Total Variation regularization, achieving a speedup of up to 155X compared to state-of-the-art methods while maintaining similar accuracy, especially effective with only 1% known data.
We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train initialization procedure is proposed specifically for image and video completion, which is demonstrated to ensure fast convergence of the completion algorithm. The tensor train framework is also shown to easily accommodate Total Variation and Tikhonov regularization due to their low-rank tensor train representations. Image and video inpainting experiments verify the superiority of the proposed scheme in terms of both speed and scalability, where a speedup of up to 155X is observed compared to state-of-the-art tensor completion methods at a similar accuracy. Moreover, we demonstrate the proposed scheme is especially advantageous over existing algorithms when only tiny portions (say, 1%) of the to-be-completed images/videos are known.