## A range characterization of the single-quadrant ADRT

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Weilin Li, Kui Ren and Donsub Rim
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## Abstract:

This work characterizes the range of the single-quadrant approximate discrete Radon transform (ADRT) of square images. The characterization follows from a set of linear constraints on the codomain. We show that for data satisfying these constraints, the exact and fast inversion formula by Rim [Appl. Math. Lett. 102 (2020), 106159] yields a square image in a stable manner. The range characterization is obtained by first showing that the ADRT is a bijection between images supported on infinite half-strips, then identifying the linear subspaces that stay finitely supported under the inversion formula.## References

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## Additional Information

**Weilin Li**- Affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
- MR Author ID: 1052146
- ORCID: 0000-0003-0345-4713
- Email: weilinli@cims.nyu.edu
**Kui Ren**- Affiliation: Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027
- MR Author ID: 711179
- ORCID: 0000-0001-6463-4561
- Email: kr2002@columbia.edu
**Donsub Rim**- Affiliation: Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, Missouri 63105
- MR Author ID: 990462
- ORCID: 0000-0002-6721-2070
- Email: rim@wustl.edu
- Received by editor(s): October 18, 2020
- Received by editor(s) in revised form: March 7, 2022
- Published electronically: August 31, 2022
- Additional Notes: The first author was supported by AMS Simons Travel grant. The work of the second author was partially supported by the National Science Foundation through grants DMS-1913309 and DMS-1937254. The work of the third author was partially supported by the Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics under Award Number FA9550-17-1-0195 and AFOSR MURI on multi-information sources of multi-physics systems under Award Number FA9550-15-1-0038
- © Copyright 2022 American Mathematical Society
- Journal: Math. Comp.
**92**(2023), 283-306 - MSC (2020): Primary 44A12, 65R10, 92C55, 68U05, 15A04
- DOI: https://doi.org/10.1090/mcom/3750
- MathSciNet review: 4496966