2017/08/14 by Canyi Lu, Jiashi Feng, Lu, Canyi +9 · 6 citations
Computer Science · Engineering · Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications #cs.CV
paper · pdf · doi:10.48550/arxiv.1708.04181
IEEE International Conference on Computer Vision and Pattern Recognition (CVPR, 2016)
openalex created_date 2016/06/24 · openalex publication_date 2017/08/14 · arxiv created 2018/05/26 · arxiv updated 2018/05/29 · openalex updated_date 2026/07/28
This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin 2011) and its induced tensor tubal rank and tensor nuclear norm. Consider that we have a 3-way tensor X∈ℝn1× n2× n3 such that X=L0+E0, where L0 has low tubal rank and E0 is sparse. Is that possible to recover both components? In this work, we prove that under certain suitable assumptions, we can recover both the low-rank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the ℓ1-norm, i.e., min_L, E ‖L‖_*+λ‖E‖1, s.t. X=L+E, where λ= 1/√(max(n1,n2)n3). Interestingly, TRPCA involves RPCA as a special case when n3=1 and thus it is a simple and elegant tensor extension of RPCA. Also numerical experiments verify our theory and the application for the image denoising demonstrates the effectiveness of our method.