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Radon Transform--Gaussian


RadonGaussian
R(p,tau)=int_(-infty)^inftyint_(-infty)^infty[1/(sigmasqrt(2pi))e^(-(x^2+y^2)/(2sigma^2))]delta[y-(tau+px)]dydx
(1)
=1/(sigmasqrt(2pi))int_(-infty)^inftye^(-[x^2+(tau+px)^2]/2(sigma^2))dx
(2)
=1/(sqrt(1+p^2))e^(-t^2/[2(1+p^2)sigma^2]).
(3)

See also

Radon Transform, Radon Transform--Cylinder, Radon Transform--Delta Function, Radon Transform--Square

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Cite this as:

Weisstein, Eric W. "Radon Transform--Gaussian." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RadonTransformGaussian.html

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