Key result
ADRT spectral decomposition enables formal image inversion with order N^2 log^2 N complexity.
The study provides an explicit spectral decomposition of the approximate discrete Radon transform (ADRT), allowing for formal inversion of an N x N image with O(N^2 log^2 N) complexity.
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 × N N × N image can be formally inverted with complexity O(N² 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.
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Li et al. (2026) studied this question. The explicit spectral decomposition of the approximate discrete Radon transform (ADRT) enables formal inversion of an N x N image with complexity O(N^2 log^2 N).
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