Lipschitz Stability of Travel Time Data
We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance functions from the entire space, measured on the chosen closed subset. The case of a Riemannian manifold with boundary with the boundary as the measurement set appears is a classical geometric inverse problem arising from Gel'fand's inverse boundary spectral problem. Examples of spaces satisfying our assumptions include some non-simple Riemannian manifolds, Euclidean domains with non-trivial topology, and metric trees.
Authors
- Teemu Saksala (ORCID: https://orcid.org/0000-0002-3785-9623)
- Matti Lassas (ORCID: https://orcid.org/0000-0003-2043-3156)
- Antti Kykkänen (ORCID: https://orcid.org/0009-0001-3867-9480)
- Joonas Ilmavirta (ORCID: https://orcid.org/0000-0002-2399-0911)
- Andrew Shedlock
Institutions
- Statistics Finland (FI)
- University of Helsinki (FI)
- North Carolina State University (US)
- Rice University (US)
- University of Jyväskylä (FI)
Publication Details
- Journal
- Journal of Geometric Analysis
- Published
- 2025-06-28
- DOI
- https://doi.org/10.1007/s12220-025-02084-3
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Helsingin Yliopisto
- European Commission
- Academy of Finland
- Suomalainen Tiedeakatemia
- Directorate for Mathematical and Physical Sciences
- European Research Council
- Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta