title: The Twist Tensor Nuclear Norm for Video Completion.
abstract: In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. 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 nonstationary 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.
authors.forename: Wenrui
authors.initials: W
authors.lastname: Hu
authors.forename: Dacheng
authors.initials: D
authors.lastname: Tao
authors.forename: Wensheng
authors.initials: W
authors.lastname: Zhang
authors.forename: Yuan
authors.initials: Y
authors.lastname: Xie
authors.forename: Yehui
authors.initials: Y
authors.lastname: Yang