# A New Low-Rank Tensor Model for Video Completion

arXiv: https://arxiv.org/abs/1509.02027 · HTML: https://mlsanity.com/paper/1509.02027/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2015.

## Built on by (most cited first, 3 of 3)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [A Novel Tensor Factorization-Based Method with Robustness to Inaccurate Rank Estimation](https://mlsanity.com/paper/2305.11458/) (2023)
- [Functional-Edged Network Modeling](https://mlsanity.com/paper/2404.00218/) (2024)

## Abstract (arXiv)

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm or t-TNN for short. The twist tensor denotes a 3-way tensor representation to laterally store 2D data slices in order. On one hand, t-TNN convexly relaxes the tensor multi-rank of the twist tensor in the Fourier domain, which allows an efficient computation using FFT. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a non-stationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.