{
  "id": "1002.4935",
  "version": "v3",
  "published": "2010-02-26T08:00:08.000Z",
  "updated": "2013-05-24T15:00:13.000Z",
  "title": "Multiarray Signal Processing: Tensor decomposition meets compressed sensing",
  "authors": [
    "Lek-Heng Lim",
    "Pierre Comon"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.NA",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a measure of separation between radiating sources called coherence, one could always guarantee the existence and uniqueness of a best rank-r approximation of the tensor representing the signal. We also deduce a computationally feasible variant of Kruskal's uniqueness condition, where the coherence appears as a proxy for k-rank. Problems of sparsest recovery with an infinite continuous dictionary, lowest-rank tensor representation, and blind source separation are treated in a uniform fashion. The decomposition of the measurement tensor leads to simultaneous localization and extraction of radiating sources, in an entirely deterministic manner.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-05-24T15:00:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94A12",
      "15A69",
      "41A29",
      "41A50",
      "41A52"
    ],
    "keywords": [
      "tensor decomposition meets compressed sensing",
      "multiarray signal processing",
      "blind source separation",
      "lowest-rank tensor representation",
      "radiating sources"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.crme.2010.06.005",
      "journal": "Comptes Rendus Mecanique",
      "year": 2010,
      "month": "Jun",
      "volume": 338,
      "number": 6,
      "pages": 311
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CRMec.338..311L"
    }
  }
}