A range characterization of the single-quadrant ADRT
Numerical Analysis
2022-03-23 v2 Computer Vision and Pattern Recognition
Numerical Analysis
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 [Rim, Appl. Math. Lett. 102 106159, 2020] 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.
Keywords
Cite
@article{arxiv.2010.05360,
title = {A range characterization of the single-quadrant ADRT},
author = {Weilin Li and Kui Ren and Donsub Rim},
journal= {arXiv preprint arXiv:2010.05360},
year = {2022}
}