Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY
Volume 30, Issue 4, Pages 944-954Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSVT.2019.2901311
Keywords
Optimization; Matrix decomposition; Data structures; Convex functions; Numerical models; Minimization methods; CANDECOMP; PARAFAC decomposition; image recovery; low rank tensor completion; Tucker decomposition
Categories
Funding
- National Natural Science Foundation of China [61571102, 61602091]
- Fundamental Research Funds for the Central Universities [ZYGX2014Z003, ZYGX2016J199]
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Tensor completion recovers missing components of multi-way data. The existing methods use either the Tucker rank or the CANDECOMP/PARAFAC (CP) rank in low-rank tensor optimization for data completion. In fact, these two kinds of tensor ranks represent different high-dimensional data structures. In this paper, we propose to exploit the two kinds of data structures simultaneously for image recovery through jointly minimizing the CP rank and Tucker rank in the low-rank tensor approximation. We use the alternating direction method of multipliers (ADMM) to reformulate the optimization model with two tensor ranks into its two sub-problems, and each has only one tensor rank optimization. For the two main sub-problems in the ADMM, we apply rank-one tensor updating and weighted sum of matrix nuclear norms minimization methods to solve them, respectively. The numerical experiments on some image and video completion applications demonstrate that the proposed method is superior to the state-of-the-art methods.
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