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arXiv · 2010.05360

A range characterization of the single-quadrant ADRT

Weilin Li·Kui Ren·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 [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.

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Weilin Li, Kui Ren, Donsub Rim. 2020-10-11. A range characterization of the single-quadrant ADRT. https://arxiv.org/abs/2010.05360

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