Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography

TL;DR

This paper establishes the uniqueness of the inverse problem in time-domain fluorescence diffuse optical tomography and introduces new non-iterative and iterative numerical inversion methods with demonstrated 3D reconstructions.

Contribution

It provides the first uniqueness theorem for the inverse problem in FDOT and proposes novel inversion algorithms including a non-iterative peak detection method.

Findings

Proved the uniqueness of the inverse problem in FDOT.

Developed a non-iterative inversion method based on peak detection.

Demonstrated effective 3D numerical reconstructions.

Abstract

This work considers the time-domain fluorescence diffuse optical tomography (FDOT). We recover the distribution of fluorophores in biological tissue by the boundary measurements. With the Laplace transform and the knowledge of complex analysis, we build the uniqueness theorem of this inverse problem. After that, the numerical reconstructions are considered. We introduce a non-iterative inversion strategy by peak detection and an iterative inversion algorithm under the framework of regularizing scheme, then give several numerical examples in three-dimensional space illustrating the performance of the proposed inversion schemes.