Optimal recovery of a radiating source with multiple frequencies along one line
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
Published in
Inverse Problems and ImagingDate
2020Discipline
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsCopyright
© 2020 American Institute of Mathematical Sciences
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.
Publisher
American Institute of Mathematical Sciences (AIMS)ISSN Search the Publication Forum
1930-8345Keywords
inverse source problem multispectral SPECT Laplace transform beam hardening multiplicative system theorem attenuated Radon transform uniqueness theorem PET emission computed tomography nuclear medicine. inversio-ongelmat tietokonetomografia numeerinen analyysi kuvantaminen sovellettu matematiikka positroniemissiotomografia
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/47332741
Metadata
Show full item recordCollections
Related funder(s)
Research Council of FinlandFunding program(s)
Postdoctoral Researcher, AoFAdditional 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 In ...
License
Except where otherwise noted, this item's license is described as In Copyright