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Spherical Harmonic Decomposition of an image

  1. Apr 22, 2008 #1
    Hey guys,

    1. The problem statement, all variables and given/known data
    Basically the question is to explain the meaning of a SHD of an image, specifically the image of the WMAP data of the CMB. Now i understand decomposition when it comes to functions but im not sure how to extend that to images. Is it simply that you are analysing the frequency of certain spectra and mapping that? I say that because we are supposed to explain the significance of the peaks in the decomposition of the WMAP data and i assumed that they would give information of the level of isotropy in that region.

  2. jcsd
  3. Apr 23, 2008 #2

    Ben Niehoff

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    Gold Member

    If the "image" in question is a collection of data plotted on the surface of a sphere, then it can be decomposed via spherical harmonics. This is basically a spherical analogue of Fourier decomposition of functions.

    Essentially, what you do is start with a function on the sphere whose value at a particular theta, phi is equal to the data point there. Then you find the spherical harmonic series that represents this function.
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