A1 Journal article (refereed)
Optimal recovery of a radiating source with multiple frequencies along one line (2020)

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

JYU authors or editors

Publication details

All authors or editors: Brander, Tommi; Ilmavirta, Joonas; Piiroinen, Petteri; Tyni, Teemu

Journal or series: Inverse Problems and Imaging

ISSN: 1930-8345

eISSN: 1930-8345

Publication year: 2020

Volume: 14

Issue number: 6

Pages range: 967-983

Publisher: American Institute of Mathematical Sciences (AIMS)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.3934/ipi.2020044

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/73223

Publication is parallel published: https://arxiv.org/abs/1905.08028

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.

Keywords: inverse problems; numerical analysis; applied mathematics; imaging; positron emission tomography; computed tomography

Free keywords: inverse source problem; multispectral; SPECT; Laplace transform; beam hardening; multiplicative system theorem; attenuated Radon transform; uniqueness theorem; PET; emission computed tomography; nuclear medicine.

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Related projects

Ministry reporting: Yes

VIRTA submission year: 2020

JUFO rating: 2