Regularisation and Parameter Choice Rules for Composite Linear Inverse Problems
Abstract
In this paper we propose a novel regularisation strategy for structured linear inverse problems of the form Ax=F ∘ G x = z. Instead of using the operator A or a complex scheme involving both F and G simultaneously, combining already existing and simpler regularisations for F and G allows the use of established and optimised programs for high-speed computations. As classical parameter choice rules fail in the scenario when no source conditions are known because intermediate error bounds may be unavailable, we provide both a-priori and a-posteriori rules with a convergence speed analysis given source conditions. We test the proposed method on the pre-clinical medical imaging technique of magnetic particle imaging with different choices of regularisation and on a convolution problem for an analysis of the convergence speed.
Related
- Dynamic inverse problems: Online regularisation theory
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BibTeX
@misc{brandt2026regularisation,
title = {{Regularisation and Parameter Choice Rules for Composite Linear Inverse Problems}},
author = {Christina Brandt and Patrick Horn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13483},
eprint = {2610.13483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13483},
}
RIS
TY - UNPB
TI - Regularisation and Parameter Choice Rules for Composite Linear Inverse Problems
AU - Christina Brandt
AU - Patrick Horn
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13483
UR - https://arxiv.org/abs/2610.13483
AB - In this paper we propose a novel regularisation strategy for structured linear inverse problems of the form Ax=F ∘ G x = z. Instead of using the operator A or a complex scheme involving both F and G simultaneously, combining already existing and simpler regularisations for F and G allows the use of established and optimised programs for high-speed computations. As classical parameter choice rules fail in the scenario when no source conditions are known because intermediate error bounds may be unavailable, we provide both a-priori and a-posteriori rules with a convergence speed analysis given source conditions. We test the proposed method on the pre-clinical medical imaging technique of magnetic particle imaging with different choices of regularisation and on a convolution problem for an analysis of the convergence speed.
ER -