Abstract
Many kinds of real-world data, e.g., color images, videos, etc., are represented by tensors and may often be corrupted by outliers. Tensor robust principal component analysis (TRPCA) servers as a tensorial modification of the fundamental principal component analysis (PCA) which performs well in the presence of outliers. The recently proposed TRPCA model [12] based on tubal nuclear norm (TNN) has attracted much attention due to its superiority in many applications. However, TNN is computationally expensive, limiting the application of TRPCA for large tensors. To address this issue, we first propose a new TRPCA model by adopting a factorization strategy within the framework of tensor singular value decomposition (t-SVD). An algorithm based on the non-convex augmented Lagrangian method (ALM) is developed with convergence guarantee. Effectiveness and efficiency of the proposed algorithm is demonstrated through extensive experiments on both synthetic and real datasets.
This work is partially supported by the National Natural Science Foundation of China [Grant Nos. 61872188, U1713208, 61602244, 61672287, 61702262, 61773215, 61703209].
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Notes
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The supplementary material is available at https://github.com/pingzaiwang/hitensor/blob/master/supp-ACPR2019-25.pdf.
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Wang, A., Jin, Z., Yang, J. (2020). A Factorization Strategy for Tensor Robust PCA. In: Palaiahnakote, S., Sanniti di Baja, G., Wang, L., Yan, W. (eds) Pattern Recognition. ACPR 2019. Lecture Notes in Computer Science(), vol 12046. Springer, Cham. https://doi.org/10.1007/978-3-030-41404-7_30
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