{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T13:18:55Z","timestamp":1780492735620,"version":"3.54.1"},"reference-count":109,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T00:00:00Z","timestamp":1758067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>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 (\u2113<jats:sub>2<\/jats:sub> loss, \u2113<jats:sub>1<\/jats:sub> 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.<\/jats:p>","DOI":"10.3389\/fams.2025.1594873","type":"journal-article","created":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T04:18:57Z","timestamp":1758082737000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Plug-and-play low-rank tensor completion and reconstruction algorithms with improved applicability of tensor 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