Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD

• Published in: 2014 IEEE Conference on Computer Vision and Pattern Recognition pp. 3842 - 3849
• Main Authors: Zemin Zhang, Ely, Gregory, Aeron, Shuchin, Ning Hao, Kilmer, Misha
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 01.06.2014
• Subjects: Algorithm design and analysis; Algorithms; Approximation methods; Cameras; Complexity theory; Computer vision; Electron tubes; Mathematical analysis; Matrix decomposition; Norms; Pattern recognition; Recovery; Tensile stress; Tensors; Three dimensional; Video data
• ISSN: 1063-6919; 1063-6919; 2575-7075
• DOI: 10.1109/CVPR.2014.485

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].