{
  "abstract": "Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, unweighted spectral regularizers impose a common shrinkage profile across singular components, which may excessively attenuate dominant low-rank components, and factorized variants either lack component-specific weighting or require costly singular value decompositions (SVDs). This paper proposes two weighted Schatten-$p$ tensor factorization models, termed \\WSpTFI{} and \\WSpTFII{}, under the tensor-tensor product (t-product) framework to address these limitations. \\WSpTFI{} is motivated by a factorized weighted tensor Schatten-$p$ norm identity and permits flexible, possibly asymmetric factor exponents. \\WSpTFII{} constructs a regularizer from transform-domain column-pair energies, yielding SVD-free main factor updates and a column-pruning mechanism for reducing redundant rank components. This paper further develops an iteratively reweighted alternating direction method of multipliers (ADMM)-type scheme for \\WSpTFI{} and an iteratively reweighted least squares (IRLS)--block successive upper-bound minimization (BSUM) scheme for \\WSpTFII{}. Theoretical analysis establishes the weighted factorization relation and provides a conditional limiting Karush--Kuhn--Tucker (KKT) characterization for \\WSpTFI{}. For \\WSpTFII{}, the actual damped quadratic block updates yield a quantitative sufficient-decrease mechanism for the fixed-$δ$ smoothed factor objective. This implies asymptotic regularity, and every accumulation point of the fixed-dimensional tail is stationary. Experiments on synthetic tensor completion, color-image restoration, hyperspectral inpainting, and printed-circuit-board defect detection demonstrate competitive reconstruction quality and robustness under various degradation conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14307",
  "author_total": 4,
  "authors": [
    {
      "name": "Binghao Wang"
    },
    {
      "name": "Feng Zhang"
    },
    {
      "name": "Wendong Wang"
    },
    {
      "name": "Jianjun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pnz1gygnwwp5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14307",
  "fulltext_url": null,
  "id": "7pnz1gygnwwp5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14307",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7213367204",
  "pdf_url": "https://arxiv.org/pdf/2609.14307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pnz1gygnwwp5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization",
  "title_text": "Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7pnz1gygnwwp5",
  "venue": "arXiv",
  "versions": []
}