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arXiv · 2412.05711

On an Analytical Inversion Formula for the Modulo Radon Transform

Matthias Beckmann·Carla Dittert
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Abstract

This paper proves a novel analytical inversion formula for the so-called modulo Radon transform (MRT), which models a recently proposed approach to one-shot high dynamic range tomography. It is based on the solution of a Poisson problem linking the Laplacian of the Radon transform (RT) of a function to its MRT in combination with the classical filtered back projection formula for inverting the RT. Discretizing the inversion formula using Fourier techniques leads to our novel Laplacian Modulo Unfolding - Filtered Back Projection algorithm, in short LMU-FBP, to recover a function from fully discrete MRT data. Our theoretical findings are finally supported by numerical experiments.

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Matthias Beckmann, Carla Dittert. 2024-12-07. On an Analytical Inversion Formula for the Modulo Radon Transform. https://arxiv.org/abs/2412.05711

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