# The Modulo Radon Transform: Theory, Algorithms and Applications

arXiv: https://arxiv.org/abs/2105.04194 · HTML: https://mlsanity.com/paper/2105.04194/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 50 references that are in the map.
- First posted on arXiv 10 May 2021.

## Builds on (most cited first, 3 of 3)

- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [On Unlimited Sampling and Reconstruction](https://mlsanity.com/paper/1905.03901/) (2019)

## Built on by (most cited first, 1 of 1)

- [Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude](https://mlsanity.com/paper/2510.16948/) (2025)

## Abstract (arXiv)

Recently, experiments have been reported where researchers were able to perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing multiple tomographic projections. This approach to HDR tomography has been inspired by HDR photography and inherits the same disadvantages. Taking a computational imaging approach to the HDR tomography problem, we here suggest a new model based on the Modulo Radon Transform (MRT), which we rigorously introduce and analyze. By harnessing a joint design between hardware and algorithms, we present a single-shot HDR tomography approach, which to our knowledge, is the only approach that is backed by mathematical guarantees. On the hardware front, instead of recording the Radon Transform projections that my potentially saturate, we propose to measure modulo values of the same. This ensures that the HDR measurements are folded into a lower dynamic range. On the algorithmic front, our recovery algorithms reconstruct the HDR images from folded measurements. Beyond mathematical aspects such as injectivity and inversion of the MRT for different scenarios including band-limited and approximately compactly supported images, we also provide a first proof-of-concept demonstration. To do so, we implement MRT by experimentally folding tomographic measurements available as an open source data set using our custom designed modulo hardware. Our reconstruction clearly shows the advantages of our approach for experimental data. In this way, our MRT based solution paves a path for HDR acquisition in a number of related imaging problems.