PreprintCC BY-NC-ND 4.0arXiv
An additional possibilities of the standard method of inverting the Radon transform
Abstract
The problem of inverting the Radon integral transform in finite-dimensional Euclidean space is considered. The relevance of this topic for probing issues is indicated. It is noted that for the latter direction, it is natural to consider the integrand as discontinuous function. However, the available inversion formulas are only proven for differentiable functions. Therefore, the question of obtaining formulas for discontinuous functions arises. It is set that the required results can be obtained by some modification of available proofs for smooth functions.
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BibTeX
@misc{anikonov2026additional,
title = {{An additional possibilities of the standard method of inverting the Radon transform}},
author = {D. S. Anikonov and S. G. Kazantsev and D. S. Konovalova},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17803},
eprint = {2609.17803},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17803},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - An additional possibilities of the standard method of inverting the Radon transform
AU - D. S. Anikonov
AU - S. G. Kazantsev
AU - D. S. Konovalova
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17803
UR - https://arxiv.org/abs/2609.17803
AB - The problem of inverting the Radon integral transform in finite-dimensional Euclidean space is considered. The relevance of this topic for probing issues is indicated. It is noted that for the latter direction, it is natural to consider the integrand as discontinuous function. However, the available inversion formulas are only proven for differentiable functions. Therefore, the question of obtaining formulas for discontinuous functions arises. It is set that the required results can be obtained by some modification of available proofs for smooth functions.
ER -