## 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 |
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Article number | 015004 |

Journal | Inverse Problems |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2021 |

### Bibliographical note

Funding Information: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.

Publisher Copyright:

© 2020 IOP Publishing Ltd Printed in the UK

## 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