A range characterization  of the single-quadrant ADRT

Li, Weilin; Ren, Kui; Rim, Donsub

doi:10.1090/mcom/3750

A range characterization of the single-quadrant ADRT
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by Weilin Li, Kui Ren and Donsub Rim;

Math. Comp. 92 (2023), 283-306

DOI: https://doi.org/10.1090/mcom/3750

Published electronically: August 31, 2022

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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.

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