Optimal recovery of a radiating source with multiple frequencies along one line

Tommi Olavi Brander; Joonas Ilmavirta; Petteri Piiroinen; Teemu Tyni

doi:10.3934/ipi.2020044

Optimal recovery of a radiating source with multiple frequencies along one line

Tommi Olavi Brander^*, Joonas Ilmavirta, Petteri Piiroinen, Teemu Tyni

^*Corresponding author for this work

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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.

Original language	English
Journal	Inverse Problems and Imaging
Volume	14
Issue number	6
Pages (from-to)	967–983
ISSN	1930-8337
DOIs	https://doi.org/10.3934/ipi.2020044
Publication status	Published - 2020

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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title = "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.",

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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year = "2020",

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AU - Brander, Tommi Olavi

AU - Ilmavirta, Joonas

AU - Piiroinen, Petteri

AU - Tyni, Teemu

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Inverse source problem

KW - Multispectral

KW - SPECT

KW - Laplace transform

KW - Beam hardening

KW - Multiplicative system theorem

KW - Attenuated Radon transform

KW - Uniqueness theorem

KW - PET

KW - Emission computed tomography

KW - Nuclear Medicine

U2 - 10.3934/ipi.2020044

DO - 10.3934/ipi.2020044

M3 - Journal article

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SP - 967

EP - 983

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 6

ER -

Optimal recovery of a radiating source with multiple frequencies along one line

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Keywords

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