Irregular Sampling of the Radon Transform of Bandlimited Functions

TL;DR

This paper establishes conditions under which bandlimited functions can be exactly reconstructed from irregular polar samples of their Radon transform, ensuring stable and unique solutions.

Contribution

It introduces new sampling density conditions for the Radon transform, extending classical results to irregular sampling scenarios.

Findings

Radon transform is a continuous L2-operator for certain bandlimited signals

Beurling-Malliavin condition guarantees existence and uniqueness of reconstruction

Jaffard's density condition ensures stable reconstruction

Abstract

We provide conditions for exact reconstruction of a bandlimited function from irregular polar samples of its Radon transform. First, we prove that the Radon transform is a continuous L2-operator for certain classes of bandlimited signals. We then show that the Beurling-Malliavin condition for the radial sampling density ensures existence and uniqueness of a solution. Moreover, Jaffard's density condition is sufficient for stable reconstruction.