The modulo Radon transform: theory, algorithms, and applications
File(s)
Accepted version
Author(s)
Beckmann, Matthias
Bhandari, Ayush
Krahmer, Felix
Type
Journal Article
Abstract
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 may 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 dataset 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.
Date Issued
2022-06-01
Date Acceptance
2021-11-01
Citation
SIAM Journal on Imaging Sciences, 2022, 15 (2), pp.455-490
ISSN
1936-4954
Publisher
Society for Industrial and Applied Mathematics
Start Page
455
End Page
490
Journal / Book Title
SIAM Journal on Imaging Sciences
Volume
15
Issue
2
Copyright Statement
© 2022, Society for Industrial and Applied Mathematics. Beckmann, Matthias, Ayush Bhandari, and Felix Krahmer. "The modulo Radon transform: Theory, algorithms, and applications." SIAM Journal on Imaging Sciences 15.2 (2022): 455-490.
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000821560500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
computational imaging
Computer Science
Computer Science, Artificial Intelligence
Computer Science, Software Engineering
high dynamic range
image processing
image reconstruction
Imaging Science & Photographic Technology
inverse problem
Mathematics
Mathematics, Applied
modulo nonlinearity
Physical Sciences
Radon transform
RAY
RECONSTRUCTION
Science & Technology
Technology
X-ray tomography
Publication Status
Published
Date Publish Online
2022-04-14