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Dynamic inverse problems: Online regularisation theory
Abstract
We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors converge to zero as noise, algorithmic errors, and regularisation vanish as the horizon grows. We illustrate the theory numerically with a dynamic electrical impedance tomography example.
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BibTeX
@misc{jauhiainen2026dynamic,
title = {{Dynamic inverse problems: Online regularisation theory}},
author = {Jyrki Jauhiainen and Yassine Nabou and Tuomo Valkonen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.26022},
eprint = {2605.26022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.26022},
}
RIS
TY - UNPB
TI - Dynamic inverse problems: Online regularisation theory
AU - Jyrki Jauhiainen
AU - Yassine Nabou
AU - Tuomo Valkonen
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2605.26022
UR - https://arxiv.org/abs/2605.26022
AB - We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors converge to zero as noise, algorithmic errors, and regularisation vanish as the horizon grows. We illustrate the theory numerically with a dynamic electrical impedance tomography example.
ER -