Radon Transform--Gaussian

$\begin{figure}\begin{center}\BoxedEPSF{radon_gaussian.epsf scaled 890}\end{center}\end{figure}$

$\displaystyle R(p, \tau)$	$\textstyle =$	$\displaystyle \int_{-\infty}^\infty \int_{-\infty}^\infty \left[{{1\over\sigma\sqrt{2\pi}} e^{-(x^2+y^2)/2\sigma^2}}\right]\delta[y-(\tau+px)]\,dy\,dx$
	$\textstyle =$	$\displaystyle {1\over\sigma\sqrt{2\pi}} \int_{-\infty}^\infty e^{-[x^2+(\tau+px)^2]/2\sigma^2]}\,dx$
	$\textstyle =$	$\displaystyle {1\over\sqrt{1+p^2}} e^{-t^2/[2(1+p^2)\sigma^2]}.$