Spherical Harmonic Decomposition of an image

[FunkyDwarf]

Hey guys,

Homework Statement

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 I am 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.

Cheers
-Z

 

[Ben Niehoff]

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.