期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 33, 期 11, 页码 6916-6930出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2021.3083931
关键词
Tensors; Matrix decomposition; Correlation; Nonhomogeneous media; Minimization; Transmission line measurements; Biomedical measurement; CANDECOMP; PARAFAC (CP) decomposition; factor smooth prior; low-rank tensor completion (LRTC); multilayer sparsity (MLS) constraints; subspace structured sparsity
类别
资金
- National Natural Science Foundation of China (NSFC) [61771391]
- Key Research and Development Plan of Shaanxi Province [2020ZDLGY07-11]
- Science, Technology and Innovation Commission of Shenzhen Municipality [JCYJ20170815162956949, JCYJ20180306171146740]
- Natural Science Basic Research Plan in Shaanxi Province of China [2018JM6056]
- Sejong University
This paper introduces a new multilayer sparsity-based tensor decomposition method for low-rank tensor completion. By encoding the structured sparsity of a tensor through multiple-layer representation and introducing a new sparsity insight concept, it achieves a refined description of factor/subspace sparsity.
Existing methods for tensor completion (TC) have limited ability for characterizing low-rank (LR) structures. To depict the complex hierarchical knowledge with implicit sparsity attributes hidden in a tensor, we propose a new multilayer sparsity-based tensor decomposition (MLSTD) for the low-rank tensor completion (LRTC). The method encodes the structured sparsity of a tensor by the multiple-layer representation. Specifically, we use the CANDECOMP/PARAFAC (CP) model to decompose a tensor into an ensemble of the sum of rank-1 tensors, and the number of rank-1 components is easily interpreted as the first-layer sparsity measure. Presumably, the factor matrices are smooth since local piecewise property exists in within-mode correlation. In subspace, the local smoothness can be regarded as the second-layer sparsity. To describe the refined structures of factor/subspace sparsity, we introduce a new sparsity insight of subspace smoothness: a self-adaptive low-rank matrix factorization (LRMF) scheme, called the third-layer sparsity. By the progressive description of the sparsity structure, we formulate an MLSTD model and embed it into the LRTC problem. Then, an effective alternating direction method of multipliers (ADMM) algorithm is designed for the MLSTD minimization problem. Various experiments in RGB images, hyperspectral images (HSIs), and videos substantiate that the proposed LRTC methods are superior to state-of-the-art methods.
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