Direct inversion scheme of time-domain fluorescence diffuse optical tomography by asymptotic analysis of peak time

TL;DR

This paper introduces a direct inversion method for fluorescence diffuse optical tomography that uses peak time measurements and asymptotic analysis to accurately locate a point target.

Contribution

It develops a novel inversion scheme based on peak time asymptotics, enabling precise target localization in FDOT without iterative algorithms.

Findings

Accurately reconstructs target location using peak time data.

Demonstrates the effectiveness of the asymptotic relationship through numerical tests.

Provides a fast, direct inversion approach for FDOT.

Abstract

This paper proposes a direct inversion scheme for fluorescence diffuse optical tomography (FDOT) to reconstruct the location of a point target using the measured peak time of the temporal response functions. A sphere is defined for the target, with its radius determined by the peak time, indicating that the target lies on the sphere. By constructing a tetrahedron with edges determined by the radii, we identify the location of the target as the vertex of the tetrahedron. Asymptotically, we derive the relationship between the radius of the sphere and the peak time. Several numerical tests are implemented to demonstrate the accuracy and performance of the asymptotic relationship and the inversion scheme.