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Robust block tensor principal component analysis
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DOI：10.1016/j.sigpro.2019.107271.png)
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Abstract
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Robust tensor principal component analysis based on tensor singular value decomposition (t-SVD) is a very effective tool to extract the low rank and sparse components in multi-way signals. In this paper, instead of the tensor nuclear norm (TNN) based on t-SVD for the whole tensor, we propose using the sum of TNN for its small blocks in the same size aiming to do the extraction in a more appropriate scale. The alternating direction method of multipliers can divide the optimization model into two sub-problems, i.e. low rank tensor approximation and sparse component approximation. The iterative block tensor singular value soft thresholding and iterative soft thresholding are used to solve these two sub-problems, respectively. In numerical experiments, the results demonstrate the performance improvement of the proposal method in face image denoising, color image denoising, and illumination normalization for face images. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Tensor singular value decomposition
Tensor nuclear norm
Block tensor
Robust tensor principal component analysis
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