Radon Transform—Gaussian

Author

Eric W. Weisstein
October 16, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegralTransforms/RadonTransformGaussian.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RadonTransformGaussian.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Integral

f[x_,y_]:=Exp[-(x^2+y^2)/(2s^2)]/(s Sqrt[2π])

Integrate[f[x,τ+p x],{x,-∞,∞},Assumptions->s>0&&p∈Reals]

Plot

Plot3D[((E^(-((t^2)/(2 (1+(p^2)) (s^2)))))/(Sqrt[1+(p^2)]))/.s->1,{p,-20,20},{t,-20,20},Boxed->False,PlotPoints->50,PlotRange->{0.,1.},AxesLabel->TraditionalForm/@{p,τ,R[p,τ]}]