An explicit spectral decomposition of the ADRT
Abstract
Abstract The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit spectral decomposition of each factor. We further show that this implies—for data lying in the range of the ADRT—that the transform of an $$N \times N$$ N × N image can be formally inverted with complexity $$\mathcal {O}(N^2 \log ^2 N)$$ O ( N 2 log 2 N ) . We numerically test the accuracy of the inverse on images of moderate size and find that it is competitive with existing iterative algorithms in this special regime.
Fields of Study & Subjects
Cardiac Arrhythmias and Treatments
Lanthanide and Transition Metal Complexes
Atrial Fibrillation Management and Outcomes
Publication details
- Journal / source
- BIT Numerical Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 66
- Issue
- 2
- Publication date
- 26 May 2026
- Language
- EN