Ultrasound modulated bioluminescence tomography with a single optical measurement

Francis Chung; Tianyu Yang; Yang Yang

doi:10.1088/1361-6420/abc8aa

Ultrasound modulated bioluminescence tomography with a single optical measurement

Francis Chung, Tianyu Yang, Yang Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Ultrasound modulated bioluminescence tomography is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements (Bal et al 2016 SIAM J. Math. Anal. 48 1332). Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.

Original language	English
Article number	015004
Journal	Inverse Problems
Volume	37
Issue number	1
DOIs	https://doi.org/10.1088/1361-6420/abc8aa
State	Published - Jan 1 2021

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd Printed in the UK

Funding

The research of F Chung is partially supported by Simons Collaboration Grant 582020. The research of T Yang and Y Yang is partially supported by the NSF Grant DMS-1715178, DMS-2006881 and the start-up fund from Michigan State University. The authors are very grateful to the anonymous referees for carefully reading the original draft and for many helpful suggestions.

Funders	Funder number
Michigan State University
Simons Collaboration	582020
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-2006881, 1715178

Keywords

Bioluminescence tomography
Hybrid imaging
Internal data
Inverse source problem
Optical tomography
Radiative transfer equation
Ultrasound modulation

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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10.1088/1361-6420/abc8aa

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abstract = "Ultrasound modulated bioluminescence tomography is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements (Bal et al 2016 SIAM J. Math. Anal. 48 1332). Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.",

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AB - Ultrasound modulated bioluminescence tomography is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements (Bal et al 2016 SIAM J. Math. Anal. 48 1332). Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.

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KW - Radiative transfer equation

KW - Ultrasound modulation

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Ultrasound modulated bioluminescence tomography with a single optical measurement

Abstract

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Funding

Keywords

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