Fixed Angle Inverse Scattering for Sound Speeds Close to Constant
Abstract
We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by just one measurement. Our method is based on studying the linearized problem, which turns out to be related to the acoustic problem in photoacoustic imaging. We adapt the modified time-reversal method from [P. Stefanov and G. Uhlmann, Inverse Problems, 25 (2009), 075011] to solve the linearized problem in a stable way, and we use this to give a local uniqueness result for the nonlinear inverse problem.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Society for Industrial & Applied Mathematics (SIAM)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202308304822Use this for linking
Review status
Peer reviewed
ISSN
0036-1410
DOI
https://doi.org/10.1137/22m147640x
Language
English
Published in
SIAM Journal on Mathematical Analysis
Citation
- Ma, S., Potenciano-Machado, L., & Salo, M. (2023). Fixed Angle Inverse Scattering for Sound Speeds Close to Constant. SIAM Journal on Mathematical Analysis, 55(4), 3420-3456. https://doi.org/10.1137/22m147640x
License
Funder(s)
European Commission
Research Council of Finland
Research Council of Finland
Funding program(s)
ERC Consolidator Grant
Academy Project, AoF
Centre of Excellence, AoF
ERC Consolidator Grant
Akatemiahanke, SA
Huippuyksikkörahoitus, SA
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
The work of the authors was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging) through grants 312121 and 309963. The work of the third author was also supported by the European Research Council under Horizon 2020 grant CoG 770924.
Copyright© 2023 Society for Industrial & Applied Mathematics (SIAM)