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Nonconvex 3D array image data recovery and pattern recognition under tensor framework
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DOI：10.1016/j.patcog.2021.108311.png)
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A B S T R A C T In this paper, we present a weighted tensor Schatten-p quasi-norm ( 0 < p < 1 ) regularizer for 3D array datasets in order to recover the low-rank part and the sparse part, respectively. Corresponding algorithms associated with augmented Lagrangian multipliers are established and the constructed sequence converges to the desirable Karush-Kuhn-Tucker (KKT) point, which is mathematically validated in detail. Although the proposed weighted tensor Schatten-p quasi-norm is non-convex, it appears not only to less penalize the singular values but also to be effective in capturing the low-rank property. The main findings in this paper are the appropriate choice of p depends on specific tasks: low-rank data set recovery usually requires relatively large value of p, while sparse data set recovery needs relatively small value of p. And the weights chosen in our tensor Schatten-p quasi-norm are inversely to the singular values exponentially for promoting the sensitivity to different singular values. Experimental results for video inpainting (tensor completion), image recovery and salient object detection (tensor robust principal component analysis) have been shown that the proposed approach outperforms various latest approaches in literature. (c) 2021 Published by Elsevier Ltd.
Keyword:
Tensor completion
Tensor robust principle component analysis
T-SVD
Tensor nuclear norm
Weighted tensor schatten-p quasi-norm
期刊
IF:
7.6
论文数:
1.3W
被引数:
4.5W
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