Tensor Completion From One-Bit Observations

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Abstract
The tensor completion issues have obtained a great deal of attention in the past few years. However, the data fidelity part minimizes a squared loss function, which may be inappropriate for the case of noisy one-bit observations. In this paper, we alleviate the mentioned difficulty by drawing on the experience of matrix scenarios. Based on the convex relation to ℓ norm of the tensor multi-rank, we propose a novel optimization model trying to recover the underlying tensor in case of one-bit observations. The feasibility of this model is proved by theoretical derivations. Furthermore, an alternating direction method of multipliers based algorithm is designed to find the solution. The numerical experiments demonstrate the effectiveness of our method.
Funding Information
  • National Natural Science Foundation of China (61725202, 61632006, 61751212, 61673053, 61473034, 61771088, 91538201)
  • Beijing Municipal Science and Technology Commission, Adminitrative Commission of Zhongguancun Science Park
  • Beijing Nova Programme Interdisciplinary Cooperation Project (Z161100004916041)

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