Editing Radon transform (section)

{{Short description|Integral transform}}
[[File:Radon transform.png|thumb|upright=1.15|right|Radon transform. Maps ''f'' on the (''x'',{{nbsp}}''y'')-domain to ''Rf'' on the (''α'',{{nbsp}}''s'')-domain.]]
In [[mathematics]], the '''Radon transform''' is the [[integral transform]] which takes a function ''f'' defined on the plane to a function ''Rf'' defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the [[line integral]] of the function over that line. The transform was introduced in 1917 by [[Johann Radon]],{{sfn|Radon|1917}} who also provided a formula for the inverse transform. Radon further included formulas for the transform in [[three dimensions]], in which the integral is taken over planes (integrating over lines is known as the [[X-ray transform]]). It was later generalized to higher-dimensional [[Euclidean space]]s and more broadly in the context of [[integral geometry]]. The [[complex number|complex]] analogue of the Radon transform is known as the [[Penrose transform]]. The Radon transform is widely applicable to [[tomography]], the creation of an image from the projection data associated with cross-sectional scans of an object.