# Exact and fast inversion of the approximate discrete Radon transform from partial data

## TL;DR

This paper presents an exact and computationally efficient inversion method for a specific approximate discrete Radon transform, capable of reconstructing images from partial data with minimal computational cost.

## Contribution

It introduces a novel exact inversion formula for the approximate discrete Radon transform that operates efficiently on partial data with O(N log N) complexity.

## Key findings

- Exact inversion formula for the approximate discrete Radon transform.
- Computational complexity of O(N log N) for 2D images.
- Effective reconstruction from partial data.

## Abstract

We give an exact inversion formula for the approximate discrete Radon transform introduced in [Brady, SIAM J. Comput., 27(1), 107--119] that is of cost $O(N \log N)$ for a square 2D image with $N$ pixels and requires only partial data.