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Inverse Radon Transform

The Radon inverse transform is an integral transform that has found widespread application in the reconstruction of images from medical CT scans.

The Radon and inverse Radon transforms are implemented in the Wolfram Language as RadonTransform and InverseRadonTransform, respectively.

The Radon transform itself can be defined by

R(p,tau)[f(x,y)]=int_(-infty)^inftyf(x,tau+px)dx
(1)
=int_(-infty)^inftyint_(-infty)^inftyf(x,y)delta[y-(tau+px)]dydx
(2)
=U(p,tau),
(3)

where p is the slope of a line, tau is its intercept, and delta(x) is the delta function. The inverse Radon transform is then

f(x,y)=1/(2pi)int_(-infty)^inftyd/(dy)H[U(p,y-px)]dp,
(4)

where H is a Hilbert transform.

See also

Hilbert Transform, Radon Transform

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Cite this as:

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

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