A range characterization of the single-quadrant ADRT
This work addresses a theoretical problem in computational imaging by providing a range characterization for the ADRT, which is incremental as it builds on prior inversion formulas.
The paper characterizes the range of the single-quadrant approximate discrete Radon transform (ADRT) for square images by deriving linear constraints, showing that data satisfying these constraints allows for stable and exact inversion to produce a square image.
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.