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 inInverse Problems and Imaging
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 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.
PublisherAmerican Institute of Mathematical Sciences (AIMS)
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
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Related funder(s)Academy of Finland
Funding program(s)Postdoctoral Researcher, AoF
Additional information about fundingT.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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