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Radon Transform--Gaussian

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


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




© 1996-9 Eric W. Weisstein
1999-05-25