Editing Radon transform (section)

==Explanation==
[[File:Sinogram - Two Square Indicator Phantom.svg|thumb|upright=1.35|Radon transform of the [[indicator function]] of two squares shown in the image below. Lighter regions indicate larger function values. Black indicates zero.]]
[[File:Sinogram Source - Two Squares Phantom.svg|thumb|right|Original function is equal to one on the white region and zero on the dark region.]]
If a function<math>f</math> represents an unknown density, then the Radon transform represents the projection data obtained as the output of a tomographic scan.  Hence the inverse of the Radon transform can be used to reconstruct the original density from the projection data, and thus it forms the mathematical underpinning for [[tomographic reconstruction]], also known as [[iterative reconstruction]].

The Radon transform data is often called a '''sinogram''' because the Radon transform of an off-center point source is a sinusoid.  Consequently, the Radon transform of a number of small objects appears graphically as a number of blurred [[sine wave]]s with different amplitudes and phases.

The Radon transform is useful in [[computed axial tomography]] (CAT scan), [[barcode]] scanners, [[electron microscopy]] of [[macromolecular assemblies]] like [[virus]]es and [[protein complex]]es, [[reflection seismology]] and in the solution of hyperbolic [[partial differential equations]].[[File:Radon transform sinogram.gif|thumb|Horizontal projections through the shape result in an accumulated signal (middle bar). The sinogram on the right is generated by collecting many such projections as the shape rotates. Here, color is used to highlight which object is producing which part of the signal. Note how straight features, when aligned with the projection direction, result in stronger signals.|center|500x500px]][[File:Radon transform example.jpg|thumb|Example of reconstruction via the Radon transform using observations from different angles. The applied inversion to the projection data then reconstructs the slice image.<ref>{{Cite thesis|type=Bachelor's thesis |last=Odložilík |first=Michal |date=2023-08-31 |title=Detachment tomographic inversion study with fast visible cameras on the COMPASS tokamak |hdl=10467/111617 |language=en|publisher=Czech Technical University in Prague}}</ref>]]