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arXiv · 2412.11151

An explicit spectral decomposition of the ADRT

Weilin Li·Karl Otness·Kui Ren·Donsub Rim
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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 $N \times N$ image can be formally inverted with complexity $\mathcal{O}(N^2 \log^2 N)$. 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.

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Weilin Li, Karl Otness, Kui Ren, Donsub Rim. 2026-01-07. An explicit spectral decomposition of the ADRT. https://arxiv.org/abs/2412.11151

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