The Radon transform of a Gaussian is given by
 |  | ![int_(-infty)^inftyint_(-infty)^infty[1/(sigmasqrt(2pi))e^(-(x^2+y^2)/(2sigma^2))]delta[y-(tau+px)]dydx](/images/equations/RadonTransformGaussian/Inline3.svg) |
(1)
|
 |  | ![1/(sigmasqrt(2pi))int_(-infty)^inftye^(-[x^2+(tau+px)^2]/2(sigma^2))dx](/images/equations/RadonTransformGaussian/Inline6.svg) |
(2)
|
 |  | ![1/(sqrt(1+p^2))e^(-t^2/[2(1+p^2)sigma^2]).](/images/equations/RadonTransformGaussian/Inline9.svg) |
(3)
|
Radon Transform--Gaussian
See also
Radon Transform, Radon Transform--Cylinder, Radon Transform--Delta Function, Radon Transform--SquareExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Radon Transform--Gaussian." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RadonTransformGaussian.html