Date of Award
Doctor of Philosophy
In this paper, we study the 3D array image data completion, robust principal component analysis (PCA) and multi-view subspace clustering problems via a non-convex low-rank representation under the framework of tensors. Most recent studies of tensor-based linear models use the Tensor Nuclear Norm (TNN) as a convex surrogate of the tensor rank. However, since the tensor nuclear norm is linearly proportional to the sum of singular values, the tensor rank approximation using the tensor nuclear norm may become problematic if the ratios of the nonzero singular values are far away from $1$. This paper proposes some non-convex tensor-based functions as the objective function regularizer, aiming to achieve a better tensor low-rank approximation. A corresponding algorithm associated with the augmented Lagrangian multipliers is established. The constructed convergent sequence to the desirable Karush--Kuhn--Tucker (KKT) critical point solution is mathematically validated in detail. Extensive simulations are provided on eight benchmark image datasets and full comparisons with the latest existing approaches. The results demonstrate that our proposed method significantly outperforms those convex approaches currently available in the literature.
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