Fourier-Domain Inversion for the Modulo Radon Transform

TL;DR

This paper introduces a Fourier domain algorithm for inverting the modulo Radon transform in HDR tomography, offering lower sampling rates, robustness to noise, and hardware validation with improved dynamic range recovery.

Contribution

It presents a novel Fourier domain recovery algorithm for the modulo Radon transform with mathematical guarantees and hardware validation, advancing HDR tomography techniques.

Findings

Successful image recovery from measurements exceeding sensor dynamic range by 10x.

Lower sampling rates achieve effective reconstruction compared to previous methods.

Hardware experiments demonstrate robustness and reduced quantization noise in practical settings.

Abstract

Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these approaches inherit the limitations of multiple-exposure fusion strategy. To overcome these disadvantages, the modulo Radon transform (MRT) has been proposed. The MRT is based on a co-design of hardware and algorithms. In the hardware step, Radon transform projections are folded using modulo non-linearities. Thereon, recovery is performed by algorithmically inverting the folding, thus enabling a single-shot, HDR approach to tomography. The first steps in this topic established rigorous mathematical treatment to the problem of reconstruction from folded projections. This paper takes a step forward by proposing a new, Fourier domain recovery algorithm that is backed by mathematical guarantees. The advantages include recovery at lower sampling rates while being agnostic to modulo threshold, lower computational complexity and empirical robustness to system noise. Beyond numerical simulations, we use prototype modulo ADC based hardware experiments to validate our claims. In particular, we report image recovery based on hardware measurements up to 10 times larger than the sensor's dynamic range while benefiting with lower quantization noise ($\sim$12 dB).