{
  "annotation_id": "50949aca-1ca3-4232-a47b-b00f19e85a94",
  "date_created": "2026-03-02T18:01:24.652000Z",
  "date_modified": "2026-03-02T18:01:24.652000Z",
  "file_hash": "c94a61ada991f2674390b07069d4d64020f27621655591fd68a0072ea6b762e1",
  "private": false,
  "record": {
    "abstract": "In an inverse problem, such as the determination of brain activity given\nmagnetic field measurements outside the head, the main quantity of interest is\noften the power associated with a source. The `standard\u0027 way to determine this\nhas been to find the best linear estimate of the source and calculate the power\nassociated with this. This paper proposes an alternative method and then\nrelationship to this previous method of estimation is explored both\nalgebraically and by numerical simulation.\n  In abstract terms the problem can be stated as follows. Let H be a Hilbert\nspace with inner product \u003c, \u003e. Let L be a linear map: H-\u003eR^n. Suppose that we\nare a given data vector b in R^n such that b=Lx+e where e is a vector of random\nvariables with zero mean and given covariance matrix that represents\nmeasurement errors. The problem that is addressed in this paper is to estimate\n\u003cx,Xx\u003e where X is an operator on H (e.g. the characteristic function of a\nregion of interest).\n  Keywords: Linear inverse problem, biomagnetic inverse problem,\nmagnetoencephalography (MEG).",
    "arxiv_id": "physics/9911015",
    "authors": [
      "R Hasson"
    ],
    "categories": [
      "physics.med-ph",
      "math.NA",
      "physics.data-an"
    ],
    "title": "Is the best estimate of power equal to the power of the best estimate?",
    "url": "https://arxiv.org/abs/physics/9911015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e5c7af69-5dfc-4a67-93bc-606213caa1a9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}