## Idea

The Radon transform converts between functions on $\mathbb{R}^n$ which are integrable on all hyperplanes and functions on the space of all hyperplanes of $\mathbb{R}^n$. It corresponds to pull-push through the incidence correspondence of points and hyperplanes.

It is a real version of the Penrose transform.

It is widely used in computerized tomography.

## References

• Sigurdur Helgason, Radon Transform, second edition, Birkhäuser, New York, 1999, (book).