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Abel transform of Gaussian

  1. Aug 10, 2014 #1
    Hello. I'm wondering if anyone has a table of transforms showing the result of an Abel transform on a Gaussian distribution. I have been unable to find the solution to this. Many thanks for any help. I'm reconstructing an an image from a picture that fits a Gaussian very well, hence I'm hoping to just use an analytical solution.

  2. jcsd
  3. Aug 11, 2014 #2
    and the answer is...

    So I found the solution described as f(r) -> f(x):

    exp(-r2/2σ2) -> (2π)1/2σ*exp(-x2/2σ2)

    The added constant does not change the the value of sigma so, which doesn't make sense to me. When viewing the line itegral, shouldn't the distribution appear more narrow?
    Last edited: Aug 11, 2014
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