Singular Stability Estimates for Passive Gamma Emission Tomography of Spent Nuclear Fuel
Abstract
We study the joint recovery of attenuation and source coefficients from the attenuated X-ray transform, motivated by passive gamma emission tomography of spent nuclear fuel. Both coefficients are constant on known, disjoint disks of equal radius representing fuel rods. The surrounding moderator has known attenuation and zero source. We use tangential singularities of the data to give a sufficient condition on the geometry and coefficients for unique joint reconstruction from full data. For rods arranged on parallel rows separated by more than one rod diameter, with source coefficients uniformly bounded away from zero, we derive explicit reconstruction formulas and stability estimates for both coefficients. The estimates use a singular seminorm determined by two functionals per rod, computed from angular data near selected tangencies. Numerical experiments examine the approximation of these functionals from discretized data.
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BibTeX
@misc{heikkila2026singular,
title = {{Singular Stability Estimates for Passive Gamma Emission Tomography of Spent Nuclear Fuel}},
author = {Tommi Heikkilä and Tapio Helin and Sean Holman and Shubham R. Jathar and Jesse Railo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26276},
eprint = {2610.26276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Singular Stability Estimates for Passive Gamma Emission Tomography of Spent Nuclear Fuel
AU - Tommi Heikkilä
AU - Tapio Helin
AU - Sean Holman
AU - Shubham R. Jathar
AU - Jesse Railo
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26276
UR - https://arxiv.org/abs/2610.26276
AB - We study the joint recovery of attenuation and source coefficients from the attenuated X-ray transform, motivated by passive gamma emission tomography of spent nuclear fuel. Both coefficients are constant on known, disjoint disks of equal radius representing fuel rods. The surrounding moderator has known attenuation and zero source. We use tangential singularities of the data to give a sufficient condition on the geometry and coefficients for unique joint reconstruction from full data. For rods arranged on parallel rows separated by more than one rod diameter, with source coefficients uniformly bounded away from zero, we derive explicit reconstruction formulas and stability estimates for both coefficients. The estimates use a singular seminorm determined by two functionals per rod, computed from angular data near selected tangencies. Numerical experiments examine the approximation of these functionals from discretized data.
ER -