On an Analytical Inversion Formula for the Modulo Radon Transform

TL;DR

This paper introduces a new analytical inversion formula for the modulo Radon transform, enabling high dynamic range tomography with a novel algorithm supported by numerical experiments.

Contribution

It presents a novel inversion formula for MRT based on a Poisson problem and develops the LMU-FBP algorithm using Fourier techniques for discrete data.

Findings

The inversion formula effectively reconstructs functions from MRT data.

The LMU-FBP algorithm performs well in numerical experiments.

The approach advances high dynamic range tomography methods.

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.