Optimal recovery of a radiating source with multiple frequencies along one line
Abstract
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
American Institute of Mathematical Sciences (AIMS)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202012157168Use this for linking
Review status
Peer reviewed
ISSN
1930-8345
DOI
https://doi.org/10.3934/ipi.2020044
Language
English
Published in
Inverse Problems and Imaging
Citation
- Brander, T., Ilmavirta, J., Piiroinen, P., & Tyni, T. (2020). Optimal recovery of a radiating source with multiple frequencies along one line. Inverse Problems and Imaging, 14(6), 967-983. https://doi.org/10.3934/ipi.2020044
License
Funder(s)
Research Council of Finland
Funding program(s)
Postdoctoral Researcher, AoF
Tutkijatohtori, SA
Additional information about funding
T.B. was partially funded by grant no. 4002-00123 from the Danish Council for Independent Research | Natural Sciences and partially by the Research Council of Norway through the FRIPRO Toppforsk project "Waves and nonlinear phenomena". J.I. was supported by the Academy of Finland (decision 295853). T.T. was supported by the Academy of Finland (application number 312123, Centre of Excellence of Inverse Modelling and Imaging 2018–2025).
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