Fourier-domain inversion for the modulo Radon transform
File(s)
Accepted version
Author(s)
Beckmann, Matthias
Bhandari, Ayush
Iske, Meira
Type
Journal Article
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 (∼12 dB).
Date Issued
2024-01-01
Date Acceptance
2024-04-01
Citation
IEEE Transactions on Computational Imaging, 2024, 10, pp.653-665
ISSN
2333-9403
Publisher
Institute of Electrical and Electronics Engineers
Start Page
653
End Page
665
Journal / Book Title
IEEE Transactions on Computational Imaging
Volume
10
Copyright Statement
Copyright © 2024 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Subjects
Engineering
Engineering, Electrical & Electronic
high dynamic range
Imaging Science & Photographic Technology
modulo non-linearity
Radon transform
sampling theory
X-ray computerized tomography
Publication Status
Published
Date Publish Online
2024-04-15