A Novel Regularized Model for Third-Order Tensor Completion

Inspired by the accuracy and efficiency of the \gamma-norm of a matrix, which is closer to the original rank minimization problem than nuclear norm minimization (NNM), we generalize the \gamma-norm of a matrix to tensors and propose a new tensor completion approach within the tensor singular value d...

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Bibliographic Details
Published in:	IEEE transactions on signal processing 2021, Vol.69, p.3473-3483
Main Authors:	Yang, Yi, Han, Lixin, Liu, Yuanzhen, Zhu, Jun, Yan, Hong
Format:	Article
Language:	eng
Subjects:	Accuracy Algorithms Approximation algorithms Convex functions Cubic equations Lagrange multiplier Mathematical analysis Mathematical model Matrix decomposition Minimization Optimization Signal processing algorithms Singular value decomposition tensor <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> gamma</tex-math> </inline-formula> nuclear norm tensor completion tensor multi-rank approximation tensor singular value decomposition (t-svd) Tensors
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Summary:	Inspired by the accuracy and efficiency of the \gamma-norm of a matrix, which is closer to the original rank minimization problem than nuclear norm minimization (NNM), we generalize the \gamma-norm of a matrix to tensors and propose a new tensor completion approach within the tensor singular value decomposition (t-svd) framework. An efficient algorithm, which combines the augmented Lagrange multiplier and closed-resolution of a cubic equation, was developed to solve the associated nonconvex tensor multi-rank minimization problem. Experimental results show that the proposed approach has an advantage over current state of the art algorithms in recovery accuracy.
ISSN:	1053-587X 1941-0476