2015/09/07 by Wenrui Hu, Dacheng Tao, Hu, Wenrui +7 · 16 citations
Computer Science · Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Algebra over a field #Algorithm #Circulant matrix #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Eigenvalues and eigenvectors #FOS: Computer and information sciences #Geometry #Mathematics #Matrix norm #Physics #Pure mathematics #Sparse and Compressive Sensing Techniques #Tensor (intrinsic definition) #Tensor decomposition and applications #Twist #cs.CV
paper · pdf · doi:10.48550/arxiv.1509.02027
published in arXiv (Cornell University) (Cornell University) · 8 pages, 11 figures, 1 table
arxiv created 2015/09/07 · openalex publication_date 2015/09/07 · arxiv updated 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.