Presentation + Paper
20 June 2024 Considerations on the search of a fast non-iterative inverse discrete Radon transform
Óscar Gómez-Cárdenes, José Gil Marichal-Hernández, Fernando Luis Rosa-González, Jung-Young Son, Rafael Pérez Jiménez
Author Affiliations +
Abstract
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.
Conference Presentation
(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.
Óscar Gómez-Cárdenes, José Gil Marichal-Hernández, Fernando Luis Rosa-González, Jung-Young Son, and Rafael Pérez Jiménez "Considerations on the search of a fast non-iterative inverse discrete Radon transform", Proc. SPIE 13000, Real-time Processing of Image, Depth, and Video Information 2024, 130000K (20 June 2024); https://doi.org/10.1117/12.3021992
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KEYWORDS
Radon transform

Computational complexity theory

Inverse imaging problems

Inverse problem on medical image

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