Dual Radon transform

Summary

The dual Radon transform, or back-projection, acts on functions $g$ on the set of hyperplanes. Its value at a point $x$ of $\R^n$ is the integral of $g$ over all hyperplanes through $x$. It is the formal adjoint of the Radon transform for the natural measures. It is not the inverse of the Radon transform, but the Radon inversion formula writes the inverse as the dual transform composed with a filter. In tomography this is the back-projection step of filtered back-projection.