{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "BV0NXXGQZB"
    }
  ],
  "body": "\n## Summary\n\nA biorthogonal wavelet is a pair of wavelets $\\psi$ and $\\tilde\\psi$ whose dilated and translated copies are dual to each other.\nIt replaces a single wavelet whose copies are orthonormal.\nOne family is used to compute the coefficients of a function and the other to rebuild it.\nGiving up orthogonality allows wavelets that are both compactly supported and symmetric.\nAmong real orthonormal wavelets, only the [[Haar wavelet|JW5PA9XA7F]] has both properties.\nBiorthogonal wavelets are used in image compression, for example in the JPEG 2000 standard.\n\n## Explanations\n\n### L1 human\n\nWith an orthonormal wavelet, the same function is used to measure a signal and to rebuild it.\nA biorthogonal wavelet splits these two jobs between two different functions, an analysis wavelet and a synthesis wavelet.\nThe two families fit together like a basis and its dual basis in linear algebra: each analysis function sees exactly one synthesis function and is blind to all the others.\nThis extra freedom lets designers make both functions symmetric and short, which avoids visible distortions in compressed images.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "42C40",
      "42C15",
      "65T60"
    ],
    "name": "Biorthogonal wavelet",
    "same_as": {
      "wikidata": "Q4915256",
      "wikipedia": "Biorthogonal wavelet"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Biorthogonal_wavelet"
      }
    ],
    "specializes": [
      "4PZ35C0GV3"
    ],
    "tag": "Q7PENKTFHA"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/Q7PENKTFHA/",
  "links": [
    {
      "field": "specializes",
      "target": "4PZ35C0GV3"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/Q7PENKTFHA.md",
  "msc": [
    "42C40",
    "42C15",
    "65T60"
  ],
  "name": "Biorthogonal wavelet",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/Q7P/Q7PENKTFHA.md",
  "status": null,
  "tag": "Q7PENKTFHA",
  "uri": "m2://Q7PENKTFHA",
  "url": "https://tamnd.github.io/math2/wiki/biorthogonal-wavelet/",
  "writing": {
    "tag": "Q7PENKTFHA",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}