Discrete non-abelian X-ray transforms
Functional Analysis
2025-10-14 v1 Mathematical Physics
math.MP
Abstract
We define a discrete version of the non-abelian X-ray transform, going back in particular to Manakov, Zakharov (1981) and Strichartz (1982). We extend to this transform non-overdetermined reconstruction results obtained for the abelian case in the recent article by Novikov, Sharma (2025). In addition, we establish relations with the continuous non-abelian X-ray transform. In this respect, our results include an explicit and exact non-overdetermined layer-stripping reconstruction procedure for piecewise constant matrix-valued functions from their continuous non-abelian X-ray transform. To our knowledge, this result is new even for the classical X-ray transform.
Cite
@article{arxiv.2510.09611,
title = {Discrete non-abelian X-ray transforms},
author = {Pranav Gupta and Roman Novikov},
journal= {arXiv preprint arXiv:2510.09611},
year = {2025}
}