AUTHOR=Mukai Manabu , Hontani Hidekata , Yokota Tatsuya 

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

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 11 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1594873

DOI=10.3389/fams.2025.1594873

ISSN=2297-4687

ABSTRACT=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 (ℓ2 loss, ℓ1 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.