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Date Available

4-29-2026

Year of Publication

2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Mathematics

Faculty

Francis Chung

Faculty

Bertrand Guillou

Abstract

Inverse problems for the radiative transport equation (RTE) arise in a wide range of imaging applications, including optical tomography and problems motivated by non-line-of-sight imaging. Classical reconstruction methods rely heavily on ballistic, or unscattered, photons and typically require full boundary access, leading to severe instability and limited applicability in geometrically constrained settings. This dissertation investigates inverse radiative transport problems with restricted boundary data and develops reconstruction techniques based on scattered photons. The central focus of this work is the analysis and isolation of the single-collision term in the collision expansion of solutions to the RTE. By exploiting its distinct analytical structure, we derive explicit algebraic reconstruction formulas that allow for pointwise recovery of the scattering coefficient from localized boundary measurements. These formulas yield Lipschitz-type stability results and avoid differentiation of the data, in contrast to classical X-ray transform based methods. We apply this framework to a variety of geometric configurations. The techniques developed here broaden the scope of inverse radiative transport and provide new analytical tools for imaging in geometrically constrained environments.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2026.160

Archival?

Archival

Funding Information

Fuoco Summer Research Fellowship (2024)
Max Steckler Fellowship (4 years in a row 2020-2024)
Eaves Summer Research Fellowship (2022)

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