Plug-and-play low-rank tensor completion and reconstruction algorithms with improved applicability of tensor decompositions

In this paper, we propose a new unified optimization algorithm for general tensor completion and reconstruction problems, which is formulated as an inverse problem for low-rank tensors in general linear observation models. The proposed algorithm supports at least three basic loss functions (ℓ 2 loss, ℓ 1 loss, and generalized KL divergence) and various TD models (CP, Tucker, TT, TR decompositions, non-negative matrix/tensor factorizations, and other constrained TD models). We derive the optimization algorithm based on a hierarchical combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM). We show that the proposed algorithm can solve a wide range of applications and can be easily extended to any established TD model in a plug-and-play manner.