{
  "abstract": "Sampling a multidomain tensor from limited measurements is fundamental in structured linear inverse problems. Kronecker-structured sampling avoids the full high-dimensional sensing matrix, but design remains difficult: sequential discrete methods can commit the cross-mode budget too early, whereas standard continuous greedy avoids such early commitment at the cost of repeated state-dependent gradient evaluations. We propose spectral-residual continuous greedy (\\alg) for frame-potential (FP) tensor sampling. \\alg maintains a state-dependent fractional allocation before rounding. Mode-wise Gram matrices provide safe gradient intervals for direction certification, while Shapley values prioritize unresolved gradient queries. SR-CG then applies deterministic rounding followed by path-guided exchange (PGX), which reuses the final fractional state to restrict candidate swaps and accepts only exact FP-decreasing exchanges. We establish a finite-step approximation guarantee that approaches the classical $1-1/e$ factor as direction certification becomes exact and finite-step residual error vanishes. Experiments show fewer exact gradient evaluations and better FP designs, with clearer gains on instances where the cross-mode budget allocation is difficult to determine. \\alg also achieves lower average normalized mean-squared error (NMSE) than Greedy-FP at all tested noise levels, although the reconstruction gain is smaller than the FP gain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14346",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao Li"
    },
    {
      "name": "Jie Xu"
    },
    {
      "name": "Zheng Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hkmv9sqba7gk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14346",
  "fulltext_url": null,
  "id": "4hkmv9sqba7gk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14346",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7213245806",
  "pdf_url": "https://arxiv.org/pdf/2609.14346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hkmv9sqba7gk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.14346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Spectral-Residual Continuous Greedy for Tensor Sampling",
  "title_text": "Spectral-Residual Continuous Greedy for Tensor Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/4hkmv9sqba7gk",
  "venue": "arXiv",
  "versions": []
}