ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Optimization
Volume 11 - 2025 | doi: 10.3389/fams.2025.1594873
This article is part of the Research TopicOptimization for Low-rank Data Analysis: Theory, Algorithms and ApplicationsView all 5 articles
Plug-and-Play Low-rank Tensor Completion and Reconstruction for Improving Applicability of Tensor Decompositions
Provisionally accepted
- 1Nagoya Institute of Technology, Nagoya, Japan
- 2RIKEN Center for Advanced Intelligence Project (AIP), Chuo-ku, Tokyo, Japan
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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.
Keywords: tensor decompositions, Tensor completion, tensor reconstruction, Majorization-minimization (MM), Alternating direction method of multipliers (ADMM), Plug-and-play (PnP), genelarized KL divergence
Received: 17 Mar 2025; Accepted: 18 Aug 2025.
Copyright: © 2025 Mukai, Hontani and Yokota. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Tatsuya Yokota, Nagoya Institute of Technology, Nagoya, Japan
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