{
  "abstract": "The storage and recovery of a vector of length \\(2^d\\) can become prohibitively expensive as \\(d\\) grows, a manifestation of the curse of dimensionality. For certain structured functions and multiscale quantities, the resulting discretized vectors admit compact quantized tensor train (QTT) representations after binary tensorization: a length-\\(2^d\\) vector is reshaped into a \\(d\\)-way binary tensor with low tensor-train (TT) rank. Motivated by this construction, we study compressed sensing of tensorized signals that combine bounded TT rank with sparse low-order interaction structure, using randomly sampled Walsh--Hadamard measurements. For this structured model class, we establish a uniform restricted isometry property and derive a measurement condition guaranteeing uniqueness of noiseless recovery. We also propose a structure-aware initializer for the alternating linear scheme (ALS), obtained by projecting the adjoint backprojection onto the low-order interaction space before applying TT-SVD. We prove a uniform initialization error bound whose measurement requirement, for fixed structural parameters, grows polynomially with the tensor order \\(d\\) rather than with the ambient dimension \\(2^d\\). Numerical experiments support the predicted RIP and initialization scaling and demonstrate more reliable ALS recovery.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36506",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingchun Shao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9rnmtf3z770n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36506",
  "fulltext_url": null,
  "id": "c9rnmtf3z770n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36506",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7214900548",
  "pdf_url": "https://arxiv.org/pdf/2609.36506",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9rnmtf3z770n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36506",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36506"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Compressed Sensing with Quantized Tensor Trains (QTTs)",
  "title_text": "Compressed Sensing with Quantized Tensor Trains (QTTs)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/c9rnmtf3z770n",
  "venue": "arXiv",
  "versions": []
}