Considerations on the search of a fast non-iterative inverse discrete Radon transform

The present work aims to improve on the existing solutions for inverting the discrete Radon transform (DRT) by using less data, reducing computational cost, and ensuring well-conditioned and stable algorithms for the inversion. An analytical framework and a heuristic for finding possible inverse algorithms have been proposed. The study suggests an approach for finding a fast algorithm with a complexity of O(N² log₂ N) by analyzing operation trees for consecutive input sizes. The study also discusses the impact of noise on the proposed solutions, showing that the proposed algorithms lead to a better approximation than one iteration of Press' inversion for added random error up to 40% of the signal's magnitude. However, restricting the number of quadrants used in the algorithm leads to increased error.