Abstract
In this work, we consider the tensor completion problem of an incomplete and noisy observation. We introduce a novel completion model using bilevel minimization. Therefore, bilevel model-based denoising for the tensor completion problem is proposed. The denoising and completion tasks are fully separated. The upper-level directly addresses the completion problem with the truncated nuclear norm, while the lower-level uses the sparsity prior which is characterized by the l1-norm for the denoising task. Furthermore, we propose a simple strategy to solve our bilevel optimization problem. It formulates the lower-level as a fixed-point equation and then applies a simple but efficient iterative algorithm to get the reconstructed tensor. Numerically, the superiority of the proposal is reported via several experiments conducted on real data with an extremely small subset of observed entries.
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Communicated by: Raymond H. Chan
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Mohaoui, S., Hakim, A. & Raghay, S. Tensor completion via bilevel minimization with fixed-point constraint to estimate missing elements in noisy data. Adv Comput Math 47, 10 (2021). https://doi.org/10.1007/s10444-020-09841-8
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DOI: https://doi.org/10.1007/s10444-020-09841-8